Actual source code: petscmath.h
petsc-3.7.1 2016-05-15
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      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 PetscSqrtReal(a)    sqrt(a)
     28: #define PetscExpReal(a)     exp(a)
     29: #define PetscLogReal(a)     log(a)
     30: #define PetscLog10Real(a)   log10(a)
     31: #ifdef PETSC_HAVE_LOG2
     32: #define PetscLog2Real(a)    log2(a)
     33: #endif
     34: #define PetscSinReal(a)     sin(a)
     35: #define PetscCosReal(a)     cos(a)
     36: #define PetscTanReal(a)     tan(a)
     37: #define PetscAsinReal(a)    asin(a)
     38: #define PetscAcosReal(a)    acos(a)
     39: #define PetscAtanReal(a)    atan(a)
     40: #define PetscAtan2Real(a,b) atan2(a,b)
     41: #define PetscSinhReal(a)    sinh(a)
     42: #define PetscCoshReal(a)    cosh(a)
     43: #define PetscTanhReal(a)    tanh(a)
     44: #define PetscPowReal(a,b)   pow(a,b)
     45: #define PetscCeilReal(a)    ceil(a)
     46: #define PetscFloorReal(a)   floor(a)
     47: #define PetscFmodReal(a,b)  fmod(a,b)
     48: #define PetscTGamma(a)      tgammaf(a)
     49: #elif defined(PETSC_USE_REAL_DOUBLE)
     50: #define MPIU_REAL   MPI_DOUBLE
     51: typedef double PetscReal;
     52: #define PetscSqrtReal(a)    sqrt(a)
     53: #define PetscExpReal(a)     exp(a)
     54: #define PetscLogReal(a)     log(a)
     55: #define PetscLog10Real(a)   log10(a)
     56: #ifdef PETSC_HAVE_LOG2
     57: #define PetscLog2Real(a)    log2(a)
     58: #endif
     59: #define PetscSinReal(a)     sin(a)
     60: #define PetscCosReal(a)     cos(a)
     61: #define PetscTanReal(a)     tan(a)
     62: #define PetscAsinReal(a)    asin(a)
     63: #define PetscAcosReal(a)    acos(a)
     64: #define PetscAtanReal(a)    atan(a)
     65: #define PetscAtan2Real(a,b) atan2(a,b)
     66: #define PetscSinhReal(a)    sinh(a)
     67: #define PetscCoshReal(a)    cosh(a)
     68: #define PetscTanhReal(a)    tanh(a)
     69: #define PetscPowReal(a,b)   pow(a,b)
     70: #define PetscCeilReal(a)    ceil(a)
     71: #define PetscFloorReal(a)   floor(a)
     72: #define PetscFmodReal(a,b)  fmod(a,b)
     73: #define PetscTGamma(a)      tgamma(a)
     74: #elif defined(PETSC_USE_REAL___FLOAT128)
     75: #if defined(__cplusplus)
     76: extern "C" {
     77: #endif
     78: #include <quadmath.h>
     79: #if defined(__cplusplus)
     80: }
     81: #endif
     82: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
     83: #define MPIU_REAL MPIU___FLOAT128
     84: typedef __float128 PetscReal;
     85: #define PetscSqrtReal(a)    sqrtq(a)
     86: #define PetscExpReal(a)     expq(a)
     87: #define PetscLogReal(a)     logq(a)
     88: #define PetscLog10Real(a)   log10q(a)
     89: #ifdef PETSC_HAVE_LOG2
     90: #define PetscLog2Real(a)    log2q(a)
     91: #endif
     92: #define PetscSinReal(a)     sinq(a)
     93: #define PetscCosReal(a)     cosq(a)
     94: #define PetscTanReal(a)     tanq(a)
     95: #define PetscAsinReal(a)    asinq(a)
     96: #define PetscAcosReal(a)    acosq(a)
     97: #define PetscAtanReal(a)    atanq(a)
     98: #define PetscAtan2Real(a,b) atan2q(a,b)
     99: #define PetscSinhReal(a)    sinhq(a)
    100: #define PetscCoshReal(a)    coshq(a)
    101: #define PetscTanhReal(a)    tanhq(a)
    102: #define PetscPowReal(a,b)   powq(a,b)
    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)
    107: #endif /* PETSC_USE_REAL_* */

    109: /*
    110:     Complex number definitions
    111:  */
    112: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
    113: #if !defined(PETSC_SKIP_COMPLEX)
    114: #define PETSC_HAVE_COMPLEX 1
    115: /* C++ support of complex number */
    116: #if defined(PETSC_HAVE_CUSP)
    117: #define complexlib cusp
    118: #include <cusp/complex.h>
    119: #elif defined(PETSC_HAVE_VECCUDA) && __CUDACC_VER_MAJOR__ > 6
    120: /* complex headers in thrust only available in CUDA 7.0 and above */
    121: #define complexlib thrust
    122: #include <thrust/complex.h>
    123: #else
    124: #define complexlib std
    125: #include <complex>
    126: #endif

    128: #define PetscRealPartComplex(a)      (a).real()
    129: #define PetscImaginaryPartComplex(a) (a).imag()
    130: #define PetscAbsComplex(a)           complexlib::abs(a)
    131: #define PetscConjComplex(a)          complexlib::conj(a)
    132: #define PetscSqrtComplex(a)          complexlib::sqrt(a)
    133: #define PetscPowComplex(a,b)         complexlib::pow(a,b)
    134: #define PetscExpComplex(a)           complexlib::exp(a)
    135: #define PetscLogComplex(a)           complexlib::log(a)
    136: #define PetscSinComplex(a)           complexlib::sin(a)
    137: #define PetscCosComplex(a)           complexlib::cos(a)
    138: #define PetscAsinComplex(a)          complexlib::asin(a)
    139: #define PetscAcosComplex(a)          complexlib::acos(a)
    140: #if defined(PETSC_HAVE_TANCOMPLEX)
    141: #define PetscTanComplex(a)           complexlib::tan(a)
    142: #else
    143: #define PetscTanComplex(a)           PetscSinComplex(a)/PetscCosComplex(a)
    144: #endif
    145: #define PetscSinhComplex(a)          complexlib::sinh(a)
    146: #define PetscCoshComplex(a)          complexlib::cosh(a)
    147: #if defined(PETSC_HAVE_TANHCOMPLEX)
    148: #define PetscTanhComplex(a)          complexlib::tanh(a)
    149: #else
    150: #define PetscTanhComplex(a)          PetscSinhComplex(a)/PetscCoshComplex(a)
    151: #endif

    153: #if defined(PETSC_USE_REAL_SINGLE)
    154: typedef complexlib::complex<float> PetscComplex;
    155: #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
    156: static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); }
    157: static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; }
    158: static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); }
    159: static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; }
    160: static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); }
    161: static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; }
    162: static inline PetscComplex operator/(const PetscComplex& lhs, const double& rhs) { return lhs / float(rhs); }
    163: static inline PetscComplex operator/(const double& lhs, const PetscComplex& rhs) { return float(lhs) / rhs; }
    164: static inline bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); }
    165: static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); }
    166: static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); }
    167: static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); }
    168: #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
    169: #elif defined(PETSC_USE_REAL_DOUBLE)
    170: typedef complexlib::complex<double> PetscComplex;
    171: #elif defined(PETSC_USE_REAL___FLOAT128)
    172: typedef complexlib::complex<__float128> PetscComplex; /* Notstandard and not expected to work, use __complex128 */
    173: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128;
    174: #endif  /* PETSC_USE_REAL_ */
    175: #endif  /* ! PETSC_SKIP_COMPLEX */

    177: #elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
    178: #if !defined(PETSC_SKIP_COMPLEX)
    179: #define PETSC_HAVE_COMPLEX 1
    180: #include <complex.h>

    182: #if defined(PETSC_USE_REAL_SINGLE)
    183: typedef float _Complex PetscComplex;

    185: #define PetscRealPartComplex(a)      crealf(a)
    186: #define PetscImaginaryPartComplex(a) cimagf(a)
    187: #define PetscAbsComplex(a)           cabsf(a)
    188: #define PetscConjComplex(a)          conjf(a)
    189: #define PetscSqrtComplex(a)          csqrtf(a)
    190: #define PetscPowComplex(a,b)         cpowf(a,b)
    191: #define PetscExpComplex(a)           cexpf(a)
    192: #define PetscLogComplex(a)           clogf(a)
    193: #define PetscSinComplex(a)           csinf(a)
    194: #define PetscCosComplex(a)           ccosf(a)
    195: #define PetscAsinComplex(a)          casinf(a)
    196: #define PetscAcosComplex(a)          cacosf(a)
    197: #define PetscTanComplex(a)           ctanf(a)
    198: #define PetscSinhComplex(a)          csinhf(a)
    199: #define PetscCoshComplex(a)          ccoshf(a)
    200: #define PetscTanhComplex(a)          ctanhf(a)

    202: #elif defined(PETSC_USE_REAL_DOUBLE)
    203: typedef double _Complex PetscComplex;

    205: #define PetscRealPartComplex(a)      creal(a)
    206: #define PetscImaginaryPartComplex(a) cimag(a)
    207: #define PetscAbsComplex(a)           cabs(a)
    208: #define PetscConjComplex(a)          conj(a)
    209: #define PetscSqrtComplex(a)          csqrt(a)
    210: #define PetscPowComplex(a,b)         cpow(a,b)
    211: #define PetscExpComplex(a)           cexp(a)
    212: #define PetscLogComplex(a)           clog(a)
    213: #define PetscSinComplex(a)           csin(a)
    214: #define PetscCosComplex(a)           ccos(a)
    215: #define PetscAsinComplex(a)          casin(a)
    216: #define PetscAcosComplex(a)          cacos(a)
    217: #define PetscTanComplex(a)           ctan(a)
    218: #define PetscSinhComplex(a)          csinh(a)
    219: #define PetscCoshComplex(a)          ccosh(a)
    220: #define PetscTanhComplex(a)          ctanh(a)

    222: #elif defined(PETSC_USE_REAL___FLOAT128)
    223: typedef __complex128 PetscComplex;
    224: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);

    226: #define PetscRealPartComplex(a)      crealq(a)
    227: #define PetscImaginaryPartComplex(a) cimagq(a)
    228: #define PetscAbsComplex(a)           cabsq(a)
    229: #define PetscConjComplex(a)          conjq(a)
    230: #define PetscSqrtComplex(a)          csqrtq(a)
    231: #define PetscPowComplex(a,b)         cpowq(a,b)
    232: #define PetscExpComplex(a)           cexpq(a)
    233: #define PetscLogComplex(a)           clogq(a)
    234: #define PetscSinComplex(a)           csinq(a)
    235: #define PetscCosComplex(a)           ccosq(a)
    236: #define PetscAsinComplex(a)          casinq(a)
    237: #define PetscAcosComplex(a)          cacosq(a)
    238: #define PetscTanComplex(a)           ctanq(a)
    239: #define PetscSinhComplex(a)          csinhq(a)
    240: #define PetscCoshComplex(a)          ccoshq(a)
    241: #define PetscTanhComplex(a)          ctanhq(a)

    243: #endif /* PETSC_USE_REAL_* */
    244: #elif (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
    245: #error "PETSc was configured --with-scalar-type=complex, but a language-appropriate complex library is not available"
    246: #endif /* !PETSC_SKIP_COMPLEX */
    247: #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */

    249: #if defined(PETSC_HAVE_COMPLEX)
    250: #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
    251: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
    252: #define MPIU_C_COMPLEX MPI_C_COMPLEX
    253: #else
    254: # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX)
    255:   typedef complexlib::complex<double> petsc_mpiu_c_double_complex;
    256:   typedef complexlib::complex<float> petsc_mpiu_c_complex;
    257: # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
    258:   typedef double _Complex petsc_mpiu_c_double_complex;
    259:   typedef float _Complex petsc_mpiu_c_complex;
    260: # else
    261:   typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
    262:   typedef struct {float real,imag;} petsc_mpiu_c_complex;
    263: # endif
    264: PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
    265: PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
    266: #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
    267: #endif /* PETSC_HAVE_COMPLEX */

    269: #if defined(PETSC_HAVE_COMPLEX)
    270: #  if defined(PETSC_USE_REAL_SINGLE)
    271: #    define MPIU_COMPLEX MPIU_C_COMPLEX
    272: #  elif defined(PETSC_USE_REAL_DOUBLE)
    273: #    define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
    274: #  elif defined(PETSC_USE_REAL___FLOAT128)
    275: #    define MPIU_COMPLEX MPIU___COMPLEX128
    276: #  endif /* PETSC_USE_REAL_* */
    277: #endif

    279: #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
    280: typedef PetscComplex PetscScalar;
    281: #define PetscRealPart(a)      PetscRealPartComplex(a)
    282: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
    283: #define PetscAbsScalar(a)     PetscAbsComplex(a)
    284: #define PetscConj(a)          PetscConjComplex(a)
    285: #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
    286: #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
    287: #define PetscExpScalar(a)     PetscExpComplex(a)
    288: #define PetscLogScalar(a)     PetscLogComplex(a)
    289: #define PetscSinScalar(a)     PetscSinComplex(a)
    290: #define PetscCosScalar(a)     PetscCosComplex(a)
    291: #define PetscAsinScalar(a)    PetscAsinComplex(a)
    292: #define PetscAcosScalar(a)    PetscAcosComplex(a)
    293: #define PetscTanScalar(a)     PetscTanComplex(a)
    294: #define PetscSinhScalar(a)    PetscSinhComplex(a)
    295: #define PetscCoshScalar(a)    PetscCoshComplex(a)
    296: #define PetscTanhScalar(a)    PetscTanhComplex(a)
    297: #define MPIU_SCALAR MPIU_COMPLEX

    299: /*
    300:     real number definitions
    301:  */
    302: #else /* PETSC_USE_COMPLEX */
    303: typedef PetscReal PetscScalar;
    304: #define MPIU_SCALAR MPIU_REAL

    306: #define PetscRealPart(a)      (a)
    307: #define PetscImaginaryPart(a) ((PetscReal)0.)
    308: PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;}
    309: #define PetscConj(a)          (a)
    310: #if !defined(PETSC_USE_REAL___FLOAT128)
    311: #define PetscSqrtScalar(a)    sqrt(a)
    312: #define PetscPowScalar(a,b)   pow(a,b)
    313: #define PetscExpScalar(a)     exp(a)
    314: #define PetscLogScalar(a)     log(a)
    315: #define PetscSinScalar(a)     sin(a)
    316: #define PetscCosScalar(a)     cos(a)
    317: #define PetscAsinScalar(a)    asin(a)
    318: #define PetscAcosScalar(a)    acos(a)
    319: #define PetscTanScalar(a)     tan(a)
    320: #define PetscSinhScalar(a)    sinh(a)
    321: #define PetscCoshScalar(a)    cosh(a)
    322: #define PetscTanhScalar(a)    tanh(a)
    323: #else /* PETSC_USE_REAL___FLOAT128 */
    324: #define PetscSqrtScalar(a)    sqrtq(a)
    325: #define PetscPowScalar(a,b)   powq(a,b)
    326: #define PetscExpScalar(a)     expq(a)
    327: #define PetscLogScalar(a)     logq(a)
    328: #define PetscSinScalar(a)     sinq(a)
    329: #define PetscCosScalar(a)     cosq(a)
    330: #define PetscAsinScalar(a)    asinq(a)
    331: #define PetscAcosScalar(a)    acosq(a)
    332: #define PetscTanScalar(a)     tanq(a)
    333: #define PetscSinhScalar(a)    sinhq(a)
    334: #define PetscCoshScalar(a)    coshq(a)
    335: #define PetscTanhScalar(a)    tanhq(a)
    336: #endif /* PETSC_USE_REAL___FLOAT128 */

    338: #endif /* PETSC_USE_COMPLEX */

    340: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
    341: #define PetscSignReal(a) (((a) >= 0.0) ? ((a) == 0.0 ? 0.0 : 1.0) : -1.0)
    342: #define PetscAbs(a)  (((a) >= 0) ? (a) : -(a))

    344: /* --------------------------------------------------------------------------*/

    346: /*
    347:    Certain objects may be created using either single or double precision.
    348:    This is currently not used.
    349: */
    350: typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE } PetscScalarPrecision;

    352: #if defined(PETSC_HAVE_COMPLEX)
    353: /* PETSC_i is the imaginary number, i */
    354: PETSC_EXTERN PetscComplex PETSC_i;
    355: #endif

    357: /*MC
    358:    PetscMin - Returns minimum of two numbers

    360:    Synopsis:
    361:    #include <petscmath.h>
    362:    type PetscMin(type v1,type v2)

    364:    Not Collective

    366:    Input Parameter:
    367: +  v1 - first value to find minimum of
    368: -  v2 - second value to find minimum of

    370:    Notes: type can be integer or floating point value

    372:    Level: beginner

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

    376: M*/
    377: #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))

    379: /*MC
    380:    PetscMax - Returns maxium of two numbers

    382:    Synopsis:
    383:    #include <petscmath.h>
    384:    type max PetscMax(type v1,type v2)

    386:    Not Collective

    388:    Input Parameter:
    389: +  v1 - first value to find maximum of
    390: -  v2 - second value to find maximum of

    392:    Notes: type can be integer or floating point value

    394:    Level: beginner

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

    398: M*/
    399: #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))

    401: /*MC
    402:    PetscClipInterval - Returns a number clipped to be within an interval

    404:    Synopsis:
    405:    #include <petscmath.h>
    406:    type clip PetscClipInterval(type x,type a,type b)

    408:    Not Collective

    410:    Input Parameter:
    411: +  x - value to use if within interval (a,b)
    412: .  a - lower end of interval
    413: -  b - upper end of interval

    415:    Notes: type can be integer or floating point value

    417:    Level: beginner

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

    421: M*/
    422: #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))

    424: /*MC
    425:    PetscAbsInt - Returns the absolute value of an integer

    427:    Synopsis:
    428:    #include <petscmath.h>
    429:    int abs PetscAbsInt(int v1)

    431:    Not Collective

    433:    Input Parameter:
    434: .   v1 - the integer

    436:    Level: beginner

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

    440: M*/
    441: #define PetscAbsInt(a)  (((a)<0)   ? -(a) : (a))

    443: /*MC
    444:    PetscAbsReal - Returns the absolute value of an real number

    446:    Synopsis:
    447:    #include <petscmath.h>
    448:    Real abs PetscAbsReal(PetscReal v1)

    450:    Not Collective

    452:    Input Parameter:
    453: .   v1 - the double

    456:    Level: beginner

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

    460: M*/
    461: #define PetscAbsReal(a) (((a)<0)   ? -(a) : (a))

    463: /*MC
    464:    PetscSqr - Returns the square of a number

    466:    Synopsis:
    467:    #include <petscmath.h>
    468:    type sqr PetscSqr(type v1)

    470:    Not Collective

    472:    Input Parameter:
    473: .   v1 - the value

    475:    Notes: type can be integer or floating point value

    477:    Level: beginner

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

    481: M*/
    482: #define PetscSqr(a)     ((a)*(a))

    484: /* ----------------------------------------------------------------------------*/
    485: /*
    486:      Basic constants
    487: */
    488: #if defined(PETSC_USE_REAL___FLOAT128)
    489: #define PETSC_PI                 M_PIq
    490: #elif defined(M_PI)
    491: #define PETSC_PI                 M_PI
    492: #else
    493: #define PETSC_PI                 3.14159265358979323846264338327950288419716939937510582
    494: #endif

    496: #if !defined(PETSC_USE_64BIT_INDICES)
    497: #define PETSC_MAX_INT            2147483647
    498: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
    499: #else
    500: #define PETSC_MAX_INT            9223372036854775807L
    501: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
    502: #endif

    504: #if defined(PETSC_USE_REAL_SINGLE)
    505: #  define PETSC_MAX_REAL                3.40282346638528860e+38F
    506: #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
    507: #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
    508: #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
    509: #  define PETSC_SMALL                   1.e-5
    510: #elif defined(PETSC_USE_REAL_DOUBLE)
    511: #  define PETSC_MAX_REAL                1.7976931348623157e+308
    512: #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
    513: #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
    514: #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
    515: #  define PETSC_SMALL                   1.e-10
    516: #elif defined(PETSC_USE_REAL___FLOAT128)
    517: #  define PETSC_MAX_REAL                FLT128_MAX
    518: #  define PETSC_MIN_REAL                -FLT128_MAX
    519: #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
    520: #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078e-17q
    521: #  define PETSC_SMALL                   1.e-20q
    522: #endif

    524: #define PETSC_INFINITY                PETSC_MAX_REAL/4.0
    525: #define PETSC_NINFINITY              -PETSC_INFINITY

    527: PETSC_EXTERN PetscErrorCode PetscIsInfOrNanReal(PetscReal);
    528: PETSC_EXTERN PetscErrorCode PetscIsNanReal(PetscReal);
    529: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
    530: PETSC_STATIC_INLINE PetscErrorCode PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
    531: PETSC_STATIC_INLINE PetscErrorCode PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
    532: PETSC_STATIC_INLINE PetscErrorCode PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}

    534: /*
    535:     These macros are currently hardwired to match the regular data types, so there is no support for a different
    536:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
    537:  */
    538: #define MPIU_MATSCALAR MPIU_SCALAR
    539: typedef PetscScalar MatScalar;
    540: typedef PetscReal MatReal;

    542: struct petsc_mpiu_2scalar {PetscScalar a,b;};
    543: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
    544: #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
    545: struct petsc_mpiu_2int {PetscInt a,b;};
    546: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
    547: #else
    548: #define MPIU_2INT MPI_2INT
    549: #endif

    551: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
    552: {
    553:   PetscInt result = 1;
    554:   while (power) {
    555:     if (power & 1) result *= base;
    556:     power >>= 1;
    557:     base *= base;
    558:   }
    559:   return result;
    560: }

    562: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
    563: {
    564:   PetscReal result = 1;
    565:   if (power < 0) {
    566:     power = -power;
    567:     base  = ((PetscReal)1)/base;
    568:   }
    569:   while (power) {
    570:     if (power & 1) result *= base;
    571:     power >>= 1;
    572:     base *= base;
    573:   }
    574:   return result;
    575: }

    577: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
    578: {
    579:   PetscScalar result = 1;
    580:   if (power < 0) {
    581:     power = -power;
    582:     base  = ((PetscReal)1)/base;
    583:   }
    584:   while (power) {
    585:     if (power & 1) result *= base;
    586:     power >>= 1;
    587:     base *= base;
    588:   }
    589:   return result;
    590: }

    592: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
    593: {
    594:   PetscScalar cpower = power;
    595:   return PetscPowScalar(base,cpower);
    596: }

    598: #ifndef PETSC_HAVE_LOG2
    599: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
    600: {
    601:   return PetscLogReal(n)/PetscLogReal(2.0);
    602: }
    603: #endif
    604: #endif