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 PetscTGamma(a)      tgammaf(a)
     53: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
     54: #define PetscLGamma(a)      gammaf(a)
     55: #else
     56: #define PetscLGamma(a)      lgammaf(a)
     57: #endif

     59: #elif defined(PETSC_USE_REAL_DOUBLE)
     60: #define PetscSqrtReal(a)    sqrt(a)
     61: #define PetscCbrtReal(a)    cbrt(a)
     62: #define PetscHypotReal(a,b) hypot(a,b)
     63: #define PetscAtan2Real(a,b) atan2(a,b)
     64: #define PetscPowReal(a,b)   pow(a,b)
     65: #define PetscExpReal(a)     exp(a)
     66: #define PetscLogReal(a)     log(a)
     67: #define PetscLog10Real(a)   log10(a)
     68: #define PetscLog2Real(a)    log2(a)
     69: #define PetscSinReal(a)     sin(a)
     70: #define PetscCosReal(a)     cos(a)
     71: #define PetscTanReal(a)     tan(a)
     72: #define PetscAsinReal(a)    asin(a)
     73: #define PetscAcosReal(a)    acos(a)
     74: #define PetscAtanReal(a)    atan(a)
     75: #define PetscSinhReal(a)    sinh(a)
     76: #define PetscCoshReal(a)    cosh(a)
     77: #define PetscTanhReal(a)    tanh(a)
     78: #define PetscAsinhReal(a)   asinh(a)
     79: #define PetscAcoshReal(a)   acosh(a)
     80: #define PetscAtanhReal(a)   atanh(a)
     81: #define PetscCeilReal(a)    ceil(a)
     82: #define PetscFloorReal(a)   floor(a)
     83: #define PetscFmodReal(a,b)  fmod(a,b)
     84: #define PetscTGamma(a)      tgamma(a)
     85: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
     86: #define PetscLGamma(a)      gamma(a)
     87: #else
     88: #define PetscLGamma(a)      lgamma(a)
     89: #endif

     91: #elif defined(PETSC_USE_REAL___FLOAT128)
     92: #define PetscSqrtReal(a)    sqrtq(a)
     93: #define PetscCbrtReal(a)    cbrtq(a)
     94: #define PetscHypotReal(a,b) hypotq(a,b)
     95: #define PetscAtan2Real(a,b) atan2q(a,b)
     96: #define PetscPowReal(a,b)   powq(a,b)
     97: #define PetscExpReal(a)     expq(a)
     98: #define PetscLogReal(a)     logq(a)
     99: #define PetscLog10Real(a)   log10q(a)
    100: #define PetscLog2Real(a)    log2q(a)
    101: #define PetscSinReal(a)     sinq(a)
    102: #define PetscCosReal(a)     cosq(a)
    103: #define PetscTanReal(a)     tanq(a)
    104: #define PetscAsinReal(a)    asinq(a)
    105: #define PetscAcosReal(a)    acosq(a)
    106: #define PetscAtanReal(a)    atanq(a)
    107: #define PetscSinhReal(a)    sinhq(a)
    108: #define PetscCoshReal(a)    coshq(a)
    109: #define PetscTanhReal(a)    tanhq(a)
    110: #define PetscAsinhReal(a)   asinhq(a)
    111: #define PetscAcoshReal(a)   acoshq(a)
    112: #define PetscAtanhReal(a)   atanhq(a)
    113: #define PetscCeilReal(a)    ceilq(a)
    114: #define PetscFloorReal(a)   floorq(a)
    115: #define PetscFmodReal(a,b)  fmodq(a,b)
    116: #define PetscTGamma(a)      tgammaq(a)
    117: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
    118: #define PetscLGamma(a)      gammaq(a)
    119: #else
    120: #define PetscLGamma(a)      lgammaq(a)
    121: #endif

    123: #elif defined(PETSC_USE_REAL___FP16)
    124: #define PetscSqrtReal(a)    sqrtf(a)
    125: #define PetscCbrtReal(a)    cbrtf(a)
    126: #define PetscHypotReal(a,b) hypotf(a,b)
    127: #define PetscAtan2Real(a,b) atan2f(a,b)
    128: #define PetscPowReal(a,b)   powf(a,b)
    129: #define PetscExpReal(a)     expf(a)
    130: #define PetscLogReal(a)     logf(a)
    131: #define PetscLog10Real(a)   log10f(a)
    132: #define PetscLog2Real(a)    log2f(a)
    133: #define PetscSinReal(a)     sinf(a)
    134: #define PetscCosReal(a)     cosf(a)
    135: #define PetscTanReal(a)     tanf(a)
    136: #define PetscAsinReal(a)    asinf(a)
    137: #define PetscAcosReal(a)    acosf(a)
    138: #define PetscAtanReal(a)    atanf(a)
    139: #define PetscSinhReal(a)    sinhf(a)
    140: #define PetscCoshReal(a)    coshf(a)
    141: #define PetscTanhReal(a)    tanhf(a)
    142: #define PetscAsinhReal(a)   asinhf(a)
    143: #define PetscAcoshReal(a)   acoshf(a)
    144: #define PetscAtanhReal(a)   atanhf(a)
    145: #define PetscCeilReal(a)    ceilf(a)
    146: #define PetscFloorReal(a)   floorf(a)
    147: #define PetscFmodReal(a,b)  fmodf(a,b)
    148: #define PetscTGamma(a)      tgammaf(a)
    149: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
    150: #define PetscLGamma(a)      gammaf(a)
    151: #else
    152: #define PetscLGamma(a)      lgammaf(a)
    153: #endif

    155: #endif /* PETSC_USE_REAL_* */

    157: PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
    158: {
    159:   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
    160: }

    162: #if !defined(PETSC_HAVE_LOG2)
    163: #undef PetscLog2Real
    164: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
    165: {
    166:   return PetscLogReal(a)/PetscLogReal((PetscReal)2);
    167: }
    168: #endif

    170: #if defined(PETSC_USE_REAL___FLOAT128)
    171: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
    172: #endif
    173: #if defined(PETSC_USE_REAL___FP16)
    174: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
    175: #endif

    177: /*MC
    178:    MPIU_REAL - MPI datatype corresponding to PetscReal

    180:    Notes:
    181:    In MPI calls that require an MPI datatype that matches a PetscReal or array of PetscReal values, pass this value.

    183:    Level: beginner

    185: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
    186: M*/
    187: #if defined(PETSC_USE_REAL_SINGLE)
    188: #  define MPIU_REAL MPI_FLOAT
    189: #elif defined(PETSC_USE_REAL_DOUBLE)
    190: #  define MPIU_REAL MPI_DOUBLE
    191: #elif defined(PETSC_USE_REAL___FLOAT128)
    192: #  define MPIU_REAL MPIU___FLOAT128
    193: #elif defined(PETSC_USE_REAL___FP16)
    194: #  define MPIU_REAL MPIU___FP16
    195: #endif /* PETSC_USE_REAL_* */

    197: /*
    198:     Complex number definitions
    199:  */
    200: #if defined(PETSC_HAVE_COMPLEX)
    201: #if defined(__cplusplus)
    202: /* C++ support of complex number */

    204: #define PetscRealPartComplex(a)      (a).real()
    205: #define PetscImaginaryPartComplex(a) (a).imag()
    206: #define PetscAbsComplex(a)           petsccomplexlib::abs(a)
    207: #define PetscArgComplex(a)           petsccomplexlib::arg(a)
    208: #define PetscConjComplex(a)          petsccomplexlib::conj(a)
    209: #define PetscSqrtComplex(a)          petsccomplexlib::sqrt(a)
    210: #define PetscPowComplex(a,b)         petsccomplexlib::pow(a,b)
    211: #define PetscExpComplex(a)           petsccomplexlib::exp(a)
    212: #define PetscLogComplex(a)           petsccomplexlib::log(a)
    213: #define PetscSinComplex(a)           petsccomplexlib::sin(a)
    214: #define PetscCosComplex(a)           petsccomplexlib::cos(a)
    215: #define PetscTanComplex(a)           petsccomplexlib::tan(a)
    216: #define PetscAsinComplex(a)          petsccomplexlib::asin(a)
    217: #define PetscAcosComplex(a)          petsccomplexlib::acos(a)
    218: #define PetscAtanComplex(a)          petsccomplexlib::atan(a)
    219: #define PetscSinhComplex(a)          petsccomplexlib::sinh(a)
    220: #define PetscCoshComplex(a)          petsccomplexlib::cosh(a)
    221: #define PetscTanhComplex(a)          petsccomplexlib::tanh(a)
    222: #define PetscAsinhComplex(a)         petsccomplexlib::asinh(a)
    223: #define PetscAcoshComplex(a)         petsccomplexlib::acosh(a)
    224: #define PetscAtanhComplex(a)         petsccomplexlib::atanh(a)

    226: /* TODO: Add configure tests

    228: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
    229: #undef PetscTanComplex
    230: PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
    231: {
    232:   return PetscSinComplex(z)/PetscCosComplex(z);
    233: }
    234: #endif

    236: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
    237: #undef PetscTanhComplex
    238: PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
    239: {
    240:   return PetscSinhComplex(z)/PetscCoshComplex(z);
    241: }
    242: #endif

    244: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
    245: #undef PetscAsinComplex
    246: PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
    247: {
    248:   const PetscComplex j(0,1);
    249:   return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
    250: }
    251: #endif

    253: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
    254: #undef PetscAcosComplex
    255: PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
    256: {
    257:   const PetscComplex j(0,1);
    258:   return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
    259: }
    260: #endif

    262: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
    263: #undef PetscAtanComplex
    264: PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
    265: {
    266:   const PetscComplex j(0,1);
    267:   return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
    268: }
    269: #endif

    271: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
    272: #undef PetscAsinhComplex
    273: PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
    274: {
    275:   return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
    276: }
    277: #endif

    279: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
    280: #undef PetscAcoshComplex
    281: PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
    282: {
    283:   return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
    284: }
    285: #endif

    287: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
    288: #undef PetscAtanhComplex
    289: PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
    290: {
    291:   return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
    292: }
    293: #endif

    295: */

    297: #else /* C99 support of complex number */

    299: #if defined(PETSC_USE_REAL_SINGLE)
    300: #define PetscRealPartComplex(a)      crealf(a)
    301: #define PetscImaginaryPartComplex(a) cimagf(a)
    302: #define PetscAbsComplex(a)           cabsf(a)
    303: #define PetscArgComplex(a)           cargf(a)
    304: #define PetscConjComplex(a)          conjf(a)
    305: #define PetscSqrtComplex(a)          csqrtf(a)
    306: #define PetscPowComplex(a,b)         cpowf(a,b)
    307: #define PetscExpComplex(a)           cexpf(a)
    308: #define PetscLogComplex(a)           clogf(a)
    309: #define PetscSinComplex(a)           csinf(a)
    310: #define PetscCosComplex(a)           ccosf(a)
    311: #define PetscTanComplex(a)           ctanf(a)
    312: #define PetscAsinComplex(a)          casinf(a)
    313: #define PetscAcosComplex(a)          cacosf(a)
    314: #define PetscAtanComplex(a)          catanf(a)
    315: #define PetscSinhComplex(a)          csinhf(a)
    316: #define PetscCoshComplex(a)          ccoshf(a)
    317: #define PetscTanhComplex(a)          ctanhf(a)
    318: #define PetscAsinhComplex(a)         casinhf(a)
    319: #define PetscAcoshComplex(a)         cacoshf(a)
    320: #define PetscAtanhComplex(a)         catanhf(a)

    322: #elif defined(PETSC_USE_REAL_DOUBLE)
    323: #define PetscRealPartComplex(a)      creal(a)
    324: #define PetscImaginaryPartComplex(a) cimag(a)
    325: #define PetscAbsComplex(a)           cabs(a)
    326: #define PetscArgComplex(a)           carg(a)
    327: #define PetscConjComplex(a)          conj(a)
    328: #define PetscSqrtComplex(a)          csqrt(a)
    329: #define PetscPowComplex(a,b)         cpow(a,b)
    330: #define PetscExpComplex(a)           cexp(a)
    331: #define PetscLogComplex(a)           clog(a)
    332: #define PetscSinComplex(a)           csin(a)
    333: #define PetscCosComplex(a)           ccos(a)
    334: #define PetscTanComplex(a)           ctan(a)
    335: #define PetscAsinComplex(a)          casin(a)
    336: #define PetscAcosComplex(a)          cacos(a)
    337: #define PetscAtanComplex(a)          catan(a)
    338: #define PetscSinhComplex(a)          csinh(a)
    339: #define PetscCoshComplex(a)          ccosh(a)
    340: #define PetscTanhComplex(a)          ctanh(a)
    341: #define PetscAsinhComplex(a)         casinh(a)
    342: #define PetscAcoshComplex(a)         cacosh(a)
    343: #define PetscAtanhComplex(a)         catanh(a)

    345: #elif defined(PETSC_USE_REAL___FLOAT128)
    346: #define PetscRealPartComplex(a)      crealq(a)
    347: #define PetscImaginaryPartComplex(a) cimagq(a)
    348: #define PetscAbsComplex(a)           cabsq(a)
    349: #define PetscArgComplex(a)           cargq(a)
    350: #define PetscConjComplex(a)          conjq(a)
    351: #define PetscSqrtComplex(a)          csqrtq(a)
    352: #define PetscPowComplex(a,b)         cpowq(a,b)
    353: #define PetscExpComplex(a)           cexpq(a)
    354: #define PetscLogComplex(a)           clogq(a)
    355: #define PetscSinComplex(a)           csinq(a)
    356: #define PetscCosComplex(a)           ccosq(a)
    357: #define PetscTanComplex(a)           ctanq(a)
    358: #define PetscAsinComplex(a)          casinq(a)
    359: #define PetscAcosComplex(a)          cacosq(a)
    360: #define PetscAtanComplex(a)          catanq(a)
    361: #define PetscSinhComplex(a)          csinhq(a)
    362: #define PetscCoshComplex(a)          ccoshq(a)
    363: #define PetscTanhComplex(a)          ctanhq(a)
    364: #define PetscAsinhComplex(a)         casinhq(a)
    365: #define PetscAcoshComplex(a)         cacoshq(a)
    366: #define PetscAtanhComplex(a)         catanhq(a)

    368: #endif /* PETSC_USE_REAL_* */
    369: #endif /* (__cplusplus) */

    371: /*
    372:    PETSC_i is the imaginary number, i
    373: */
    374: PETSC_EXTERN PetscComplex PETSC_i;

    376: /*
    377:    Try to do the right thing for complex number construction: see
    378:    http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
    379:    for details
    380: */
    381: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
    382: {
    383: #if defined(__cplusplus)
    384:   return PetscComplex(x,y);
    385: #elif defined(_Imaginary_I)
    386:   return x + y * _Imaginary_I;
    387: #else
    388:   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),

    390:        "For each floating type there is a corresponding real type, which is always a real floating
    391:        type. For real floating types, it is the same type. For complex types, it is the type given
    392:        by deleting the keyword _Complex from the type name."

    394:        So type punning should be portable. */
    395:     union { PetscComplex z; PetscReal f[2]; } uz;

    397:     uz.f[0] = x;
    398:     uz.f[1] = y;
    399:     return uz.z;
    400:   }
    401: #endif
    402: }

    404: #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)\"")
    405: #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)\"")

    407: #if defined(PETSC_USE_REAL___FLOAT128)
    408: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
    409: #endif /* PETSC_USE_REAL___FLOAT128 */

    411: /*MC
    412:    MPIU_COMPLEX - MPI datatype corresponding to PetscComplex

    414:    Notes:
    415:    In MPI calls that require an MPI datatype that matches a PetscComplex or array of PetscComplex values, pass this value.

    417:    Level: beginner

    419: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
    420: M*/
    421: #if defined(PETSC_USE_REAL_SINGLE)
    422: #  define MPIU_COMPLEX MPI_C_COMPLEX
    423: #elif defined(PETSC_USE_REAL_DOUBLE)
    424: #  define MPIU_COMPLEX MPI_C_DOUBLE_COMPLEX
    425: #elif defined(PETSC_USE_REAL___FLOAT128)
    426: #  define MPIU_COMPLEX MPIU___COMPLEX128
    427: #elif defined(PETSC_USE_REAL___FP16)
    428: #  define MPIU_COMPLEX MPI_C_COMPLEX
    429: #endif /* PETSC_USE_REAL_* */

    431: #endif /* PETSC_HAVE_COMPLEX */

    433: /*
    434:     Scalar number definitions
    435:  */
    436: #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
    437: /*MC
    438:    MPIU_SCALAR - MPI datatype corresponding to PetscScalar

    440:    Notes:
    441:    In MPI calls that require an MPI datatype that matches a PetscScalar or array of PetscScalar values, pass this value.

    443:    Level: beginner

    445: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
    446: M*/
    447: #define MPIU_SCALAR MPIU_COMPLEX

    449: /*MC
    450:    PetscRealPart - Returns the real part of a PetscScalar

    452:    Synopsis:
    453: #include <petscmath.h>
    454:    PetscReal PetscRealPart(PetscScalar v)

    456:    Not Collective

    458:    Input Parameter:
    459: .  v - value to find the real part of

    461:    Level: beginner

    463: .seealso: PetscScalar, PetscImaginaryPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

    465: M*/
    466: #define PetscRealPart(a)      PetscRealPartComplex(a)

    468: /*MC
    469:    PetscImaginaryPart - Returns the imaginary part of a PetscScalar

    471:    Synopsis:
    472: #include <petscmath.h>
    473:    PetscReal PetscImaginaryPart(PetscScalar v)

    475:    Not Collective

    477:    Input Parameter:
    478: .  v - value to find the imaginary part of

    480:    Level: beginner

    482:    Notes:
    483:        If PETSc was configured for real numbers then this always returns the value 0

    485: .seealso: PetscScalar, PetscRealPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

    487: M*/
    488: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

    490: #define PetscAbsScalar(a)     PetscAbsComplex(a)
    491: #define PetscArgScalar(a)     PetscArgComplex(a)
    492: #define PetscConj(a)          PetscConjComplex(a)
    493: #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
    494: #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
    495: #define PetscExpScalar(a)     PetscExpComplex(a)
    496: #define PetscLogScalar(a)     PetscLogComplex(a)
    497: #define PetscSinScalar(a)     PetscSinComplex(a)
    498: #define PetscCosScalar(a)     PetscCosComplex(a)
    499: #define PetscTanScalar(a)     PetscTanComplex(a)
    500: #define PetscAsinScalar(a)    PetscAsinComplex(a)
    501: #define PetscAcosScalar(a)    PetscAcosComplex(a)
    502: #define PetscAtanScalar(a)    PetscAtanComplex(a)
    503: #define PetscSinhScalar(a)    PetscSinhComplex(a)
    504: #define PetscCoshScalar(a)    PetscCoshComplex(a)
    505: #define PetscTanhScalar(a)    PetscTanhComplex(a)
    506: #define PetscAsinhScalar(a)   PetscAsinhComplex(a)
    507: #define PetscAcoshScalar(a)   PetscAcoshComplex(a)
    508: #define PetscAtanhScalar(a)   PetscAtanhComplex(a)

    510: #else /* PETSC_USE_COMPLEX */
    511: #define MPIU_SCALAR MPIU_REAL
    512: #define PetscRealPart(a)      (a)
    513: #define PetscImaginaryPart(a) ((PetscReal)0)
    514: #define PetscAbsScalar(a)     PetscAbsReal(a)
    515: #define PetscArgScalar(a)     (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
    516: #define PetscConj(a)          (a)
    517: #define PetscSqrtScalar(a)    PetscSqrtReal(a)
    518: #define PetscPowScalar(a,b)   PetscPowReal(a,b)
    519: #define PetscExpScalar(a)     PetscExpReal(a)
    520: #define PetscLogScalar(a)     PetscLogReal(a)
    521: #define PetscSinScalar(a)     PetscSinReal(a)
    522: #define PetscCosScalar(a)     PetscCosReal(a)
    523: #define PetscTanScalar(a)     PetscTanReal(a)
    524: #define PetscAsinScalar(a)    PetscAsinReal(a)
    525: #define PetscAcosScalar(a)    PetscAcosReal(a)
    526: #define PetscAtanScalar(a)    PetscAtanReal(a)
    527: #define PetscSinhScalar(a)    PetscSinhReal(a)
    528: #define PetscCoshScalar(a)    PetscCoshReal(a)
    529: #define PetscTanhScalar(a)    PetscTanhReal(a)
    530: #define PetscAsinhScalar(a)   PetscAsinhReal(a)
    531: #define PetscAcoshScalar(a)   PetscAcoshReal(a)
    532: #define PetscAtanhScalar(a)   PetscAtanhReal(a)

    534: #endif /* PETSC_USE_COMPLEX */

    536: /*
    537:    Certain objects may be created using either single or double precision.
    538:    This is currently not used.
    539: */
    540: typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;

    542: /* --------------------------------------------------------------------------*/

    544: /*MC
    545:    PetscAbs - Returns the absolute value of a number

    547:    Synopsis:
    548: #include <petscmath.h>
    549:    type PetscAbs(type v)

    551:    Not Collective

    553:    Input Parameter:
    554: .  v - the number

    556:    Notes:
    557:     type can be integer or real floating point value

    559:    Level: beginner

    561: .seealso: PetscAbsInt(), PetscAbsReal(), PetscAbsScalar()

    563: M*/
    564: #define PetscAbs(a)  (((a) >= 0) ? (a) : (-(a)))

    566: /*MC
    567:    PetscSign - Returns the sign of a number as an integer

    569:    Synopsis:
    570: #include <petscmath.h>
    571:    int PetscSign(type v)

    573:    Not Collective

    575:    Input Parameter:
    576: .  v - the number

    578:    Notes:
    579:     type can be integer or real floating point value

    581:    Level: beginner

    583: M*/
    584: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)

    586: /*MC
    587:    PetscMin - Returns minimum of two numbers

    589:    Synopsis:
    590: #include <petscmath.h>
    591:    type PetscMin(type v1,type v2)

    593:    Not Collective

    595:    Input Parameter:
    596: +  v1 - first value to find minimum of
    597: -  v2 - second value to find minimum of

    599:    Notes:
    600:     type can be integer or floating point value

    602:    Level: beginner

    604: .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

    606: M*/
    607: #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))

    609: /*MC
    610:    PetscMax - Returns maxium of two numbers

    612:    Synopsis:
    613: #include <petscmath.h>
    614:    type max PetscMax(type v1,type v2)

    616:    Not Collective

    618:    Input Parameter:
    619: +  v1 - first value to find maximum of
    620: -  v2 - second value to find maximum of

    622:    Notes:
    623:     type can be integer or floating point value

    625:    Level: beginner

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

    629: M*/
    630: #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))

    632: /*MC
    633:    PetscClipInterval - Returns a number clipped to be within an interval

    635:    Synopsis:
    636: #include <petscmath.h>
    637:    type clip PetscClipInterval(type x,type a,type b)

    639:    Not Collective

    641:    Input Parameter:
    642: +  x - value to use if within interval [a,b]
    643: .  a - lower end of interval
    644: -  b - upper end of interval

    646:    Notes:
    647:     type can be integer or floating point value

    649:    Level: beginner

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

    653: M*/
    654: #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))

    656: /*MC
    657:    PetscAbsInt - Returns the absolute value of an integer

    659:    Synopsis:
    660: #include <petscmath.h>
    661:    int abs PetscAbsInt(int v1)

    663:    Not Collective

    665:    Input Parameter:
    666: .   v1 - the integer

    668:    Level: beginner

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

    672: M*/
    673: #define PetscAbsInt(a)  (((a)<0)   ? (-(a)) : (a))

    675: /*MC
    676:    PetscAbsReal - Returns the absolute value of an real number

    678:    Synopsis:
    679: #include <petscmath.h>
    680:    Real abs PetscAbsReal(PetscReal v1)

    682:    Not Collective

    684:    Input Parameter:
    685: .   v1 - the double

    688:    Level: beginner

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

    692: M*/
    693: #if defined(PETSC_USE_REAL_SINGLE)
    694: #define PetscAbsReal(a) fabsf(a)
    695: #elif defined(PETSC_USE_REAL_DOUBLE)
    696: #define PetscAbsReal(a) fabs(a)
    697: #elif defined(PETSC_USE_REAL___FLOAT128)
    698: #define PetscAbsReal(a) fabsq(a)
    699: #elif defined(PETSC_USE_REAL___FP16)
    700: #define PetscAbsReal(a) fabsf(a)
    701: #endif

    703: /*MC
    704:    PetscSqr - Returns the square of a number

    706:    Synopsis:
    707: #include <petscmath.h>
    708:    type sqr PetscSqr(type v1)

    710:    Not Collective

    712:    Input Parameter:
    713: .   v1 - the value

    715:    Notes:
    716:     type can be integer or floating point value

    718:    Level: beginner

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

    722: M*/
    723: #define PetscSqr(a)     ((a)*(a))

    725: /* ----------------------------------------------------------------------------*/

    727: #if defined(PETSC_USE_REAL_SINGLE)
    728: #define PetscRealConstant(constant) constant##F
    729: #elif defined(PETSC_USE_REAL_DOUBLE)
    730: #define PetscRealConstant(constant) constant
    731: #elif defined(PETSC_USE_REAL___FLOAT128)
    732: #define PetscRealConstant(constant) constant##Q
    733: #elif defined(PETSC_USE_REAL___FP16)
    734: #define PetscRealConstant(constant) constant##F
    735: #endif

    737: /*
    738:      Basic constants
    739: */
    740: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
    741: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
    742: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

    744: #if !defined(PETSC_USE_64BIT_INDICES)
    745: #define PETSC_MAX_INT            2147483647
    746: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
    747: #else
    748: #define PETSC_MAX_INT            9223372036854775807L
    749: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
    750: #endif
    751: #define PETSC_MAX_UINT16         65535

    753: #if defined(PETSC_USE_REAL_SINGLE)
    754: #  define PETSC_MAX_REAL                3.40282346638528860e+38F
    755: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
    756: #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
    757: #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
    758: #  define PETSC_SMALL                   1.e-5F
    759: #elif defined(PETSC_USE_REAL_DOUBLE)
    760: #  define PETSC_MAX_REAL                1.7976931348623157e+308
    761: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
    762: #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
    763: #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
    764: #  define PETSC_SMALL                   1.e-10
    765: #elif defined(PETSC_USE_REAL___FLOAT128)
    766: #  define PETSC_MAX_REAL                FLT128_MAX
    767: #  define PETSC_MIN_REAL                (-FLT128_MAX)
    768: #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
    769: #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078144567552953958511352539e-17Q
    770: #  define PETSC_SMALL                   1.e-20Q
    771: #elif defined(PETSC_USE_REAL___FP16)
    772: #  define PETSC_MAX_REAL                65504.0F
    773: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
    774: #  define PETSC_MACHINE_EPSILON         .0009765625F
    775: #  define PETSC_SQRT_MACHINE_EPSILON    .03125F
    776: #  define PETSC_SMALL                   5.e-3F
    777: #endif

    779: #define PETSC_INFINITY               (PETSC_MAX_REAL/4)
    780: #define PETSC_NINFINITY              (-PETSC_INFINITY)

    782: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
    783: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
    784: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
    785: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
    786: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
    787: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
    788: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
    789: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}

    791: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
    792: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
    793: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);

    795: /*
    796:     These macros are currently hardwired to match the regular data types, so there is no support for a different
    797:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
    798:  */
    799: #define MPIU_MATSCALAR MPIU_SCALAR
    800: typedef PetscScalar MatScalar;
    801: typedef PetscReal MatReal;

    803: struct petsc_mpiu_2scalar {PetscScalar a,b;};
    804: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);

    806: #if defined(PETSC_USE_64BIT_INDICES)
    807: struct petsc_mpiu_2int {PetscInt a,b;};
    808: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
    809: #else
    810: #define MPIU_2INT MPI_2INT
    811: #endif

    813: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
    814: {
    815:   PetscInt result = 1;
    816:   while (power) {
    817:     if (power & 1) result *= base;
    818:     power >>= 1;
    819:     base *= base;
    820:   }
    821:   return result;
    822: }

    824: PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
    825: {
    826:   PetscInt64 result = 1;
    827:   while (power) {
    828:     if (power & 1) result *= base;
    829:     power >>= 1;
    830:     base *= base;
    831:   }
    832:   return result;
    833: }

    835: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
    836: {
    837:   PetscReal result = 1;
    838:   if (power < 0) {
    839:     power = -power;
    840:     base  = ((PetscReal)1)/base;
    841:   }
    842:   while (power) {
    843:     if (power & 1) result *= base;
    844:     power >>= 1;
    845:     base *= base;
    846:   }
    847:   return result;
    848: }

    850: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
    851: {
    852:   PetscScalar result = (PetscReal)1;
    853:   if (power < 0) {
    854:     power = -power;
    855:     base  = ((PetscReal)1)/base;
    856:   }
    857:   while (power) {
    858:     if (power & 1) result *= base;
    859:     power >>= 1;
    860:     base *= base;
    861:   }
    862:   return result;
    863: }

    865: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
    866: {
    867:   PetscScalar cpower = power;
    868:   return PetscPowScalar(base,cpower);
    869: }

    871: /*MC
    872:     PetscLTE - Performs a less than or equal to on a given constant with a fudge for floating point numbers

    874:    Synopsis:
    875: #include <petscmath.h>
    876:    bool PetscLTE(PetscReal x,constant float)

    878:    Not Collective

    880:    Input Parameters:
    881: +   x - the variable
    882: -   b - the constant float it is checking if x is less than or equal to

    884:    Notes:
    885:      The fudge factor is the value PETSC_SMALL

    887:      The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    889:      This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    890:      floating point results.

    892:    Level: advanced

    894: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal(), PetscGTE()

    896: M*/
    897: #define PetscLTE(x,b)  ((x) <= (PetscRealConstant(b)+PETSC_SMALL))

    899: /*MC
    900:     PetscGTE - Performs a greater than or equal to on a given constant with a fudge for floating point numbers

    902:    Synopsis:
    903: #include <petscmath.h>
    904:    bool PetscGTE(PetscReal x,constant float)

    906:    Not Collective

    908:    Input Parameters:
    909: +   x - the variable
    910: -   b - the constant float it is checking if x is greater than or equal to

    912:    Notes:
    913:      The fudge factor is the value PETSC_SMALL

    915:      The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    917:      This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    918:      floating point results.

    920:    Level: advanced

    922: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal(), PetscLTE()

    924: M*/
    925: #define PetscGTE(x,b)  ((x) >= (PetscRealConstant(b)-PETSC_SMALL))

    928: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt,const PetscReal[],const PetscReal[],PetscReal*,PetscReal*);
    929: #endif