Date: 2022-03-04T17:40:00+00:00

Actual source code: petscmath.h

      1: /*

      3:     PETSc mathematics include file. Defines certain basic mathematical
      4:     constants and functions for working with single, double, and quad precision
      5:     floating point numbers as well as complex single and double.

      7:     This file is included by petscsys.h and should not be used directly.

      9: */

     11: #if !defined(PETSCMATH_H)
     12: #define PETSCMATH_H
     13: #include <math.h>
     14: #include <petscsystypes.h>

     16: /*

     18:    Defines operations that are different for complex and real numbers.
     19:    All PETSc objects in one program are built around the object
     20:    PetscScalar which is either always a real or a complex.

     22: */

     24: /*
     25:     Real number definitions
     26:  */
     27: #if defined(PETSC_USE_REAL_SINGLE)
     28: #define PetscSqrtReal(a)       sqrtf(a)
     29: #define PetscCbrtReal(a)       cbrtf(a)
     30: #define PetscHypotReal(a,b)    hypotf(a,b)
     31: #define PetscAtan2Real(a,b)    atan2f(a,b)
     32: #define PetscPowReal(a,b)      powf(a,b)
     33: #define PetscExpReal(a)        expf(a)
     34: #define PetscLogReal(a)        logf(a)
     35: #define PetscLog10Real(a)      log10f(a)
     36: #define PetscLog2Real(a)       log2f(a)
     37: #define PetscSinReal(a)        sinf(a)
     38: #define PetscCosReal(a)        cosf(a)
     39: #define PetscTanReal(a)        tanf(a)
     40: #define PetscAsinReal(a)       asinf(a)
     41: #define PetscAcosReal(a)       acosf(a)
     42: #define PetscAtanReal(a)       atanf(a)
     43: #define PetscSinhReal(a)       sinhf(a)
     44: #define PetscCoshReal(a)       coshf(a)
     45: #define PetscTanhReal(a)       tanhf(a)
     46: #define PetscAsinhReal(a)      asinhf(a)
     47: #define PetscAcoshReal(a)      acoshf(a)
     48: #define PetscAtanhReal(a)      atanhf(a)
     49: #define PetscCeilReal(a)       ceilf(a)
     50: #define PetscFloorReal(a)      floorf(a)
     51: #define PetscFmodReal(a,b)     fmodf(a,b)
     52: #define PetscCopysignReal(a,b) copysignf(a,b)
     53: #define PetscTGamma(a)         tgammaf(a)
     54: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
     55: #define PetscLGamma(a)         gammaf(a)
     56: #else
     57: #define PetscLGamma(a)         lgammaf(a)
     58: #endif

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

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

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

    159: #endif /* PETSC_USE_REAL_* */

    161: PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
    162: {
    163:   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
    164: }

    166: #if !defined(PETSC_HAVE_LOG2)
    167: #undef PetscLog2Real
    168: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
    169: {
    170:   return PetscLogReal(a)/PetscLogReal((PetscReal)2);
    171: }
    172: #endif

    174: #if defined(PETSC_USE_REAL___FLOAT128)
    175: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
    176: #endif
    177: #if defined(PETSC_USE_REAL___FP16)
    178: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
    179: #endif

    181: /*MC
    182:    MPIU_REAL - MPI datatype corresponding to PetscReal

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

    187:    Level: beginner

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

    201: /*
    202:     Complex number definitions
    203:  */
    204: #if defined(PETSC_HAVE_COMPLEX)
    205: #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
    206: /* C++ support of complex number */

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

    230: /* TODO: Add configure tests

    232: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
    233: #undef PetscTanComplex
    234: PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
    235: {
    236:   return PetscSinComplex(z)/PetscCosComplex(z);
    237: }
    238: #endif

    240: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
    241: #undef PetscTanhComplex
    242: PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
    243: {
    244:   return PetscSinhComplex(z)/PetscCoshComplex(z);
    245: }
    246: #endif

    248: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
    249: #undef PetscAsinComplex
    250: PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
    251: {
    252:   const PetscComplex j(0,1);
    253:   return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
    254: }
    255: #endif

    257: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
    258: #undef PetscAcosComplex
    259: PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
    260: {
    261:   const PetscComplex j(0,1);
    262:   return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
    263: }
    264: #endif

    266: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
    267: #undef PetscAtanComplex
    268: PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
    269: {
    270:   const PetscComplex j(0,1);
    271:   return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
    272: }
    273: #endif

    275: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
    276: #undef PetscAsinhComplex
    277: PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
    278: {
    279:   return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
    280: }
    281: #endif

    283: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
    284: #undef PetscAcoshComplex
    285: PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
    286: {
    287:   return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
    288: }
    289: #endif

    291: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
    292: #undef PetscAtanhComplex
    293: PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
    294: {
    295:   return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
    296: }
    297: #endif

    299: */

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

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

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

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

    372: #endif /* PETSC_USE_REAL_* */
    373: #endif /* (__cplusplus) */

    375: /*
    376:    PETSC_i is the imaginary number, i
    377: */
    378: PETSC_EXTERN PetscComplex PETSC_i;

    380: /*
    381:    Try to do the right thing for complex number construction: see
    382:    http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
    383:    for details
    384: */
    385: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
    386: {
    387: #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
    388:   return PetscComplex(x,y);
    389: #elif defined(_Imaginary_I)
    390:   return x + y * _Imaginary_I;
    391: #else
    392:   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),

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

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

    401:     uz.f[0] = x;
    402:     uz.f[1] = y;
    403:     return uz.z;
    404:   }
    405: #endif
    406: }

    408: #define MPIU_C_COMPLEX MPI_C_COMPLEX PETSC_DEPRECATED_MACRO("GCC warning \"MPIU_C_COMPLEX macro is deprecated use MPI_C_COMPLEX (since version 3.15)\"")
    409: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX PETSC_DEPRECATED_MACRO("GCC warning \"MPIU_C_DOUBLE_COMPLEX macro is deprecated use MPI_C_DOUBLE_COMPLEX (since version 3.15)\"")

    411: #if defined(PETSC_USE_REAL___FLOAT128)
    412: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
    413: #endif /* PETSC_USE_REAL___FLOAT128 */

    415: /*MC
    416:    MPIU_COMPLEX - MPI datatype corresponding to PetscComplex

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

    421:    Level: beginner

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

    435: #endif /* PETSC_HAVE_COMPLEX */

    437: /*
    438:     Scalar number definitions
    439:  */
    440: #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
    441: /*MC
    442:    MPIU_SCALAR - MPI datatype corresponding to PetscScalar

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

    447:    Level: beginner

    449: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
    450: M*/
    451: #define MPIU_SCALAR MPIU_COMPLEX

    453: /*MC
    454:    PetscRealPart - Returns the real part of a PetscScalar

    456:    Synopsis:
    457: #include <petscmath.h>
    458:    PetscReal PetscRealPart(PetscScalar v)

    460:    Not Collective

    462:    Input Parameter:
    463: .  v - value to find the real part of

    465:    Level: beginner

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

    469: M*/
    470: #define PetscRealPart(a)      PetscRealPartComplex(a)

    472: /*MC
    473:    PetscImaginaryPart - Returns the imaginary part of a PetscScalar

    475:    Synopsis:
    476: #include <petscmath.h>
    477:    PetscReal PetscImaginaryPart(PetscScalar v)

    479:    Not Collective

    481:    Input Parameter:
    482: .  v - value to find the imaginary part of

    484:    Level: beginner

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

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

    491: M*/
    492: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

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

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

    538: #endif /* PETSC_USE_COMPLEX */

    540: /*
    541:    Certain objects may be created using either single or double precision.
    542:    This is currently not used.
    543: */
    544: typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;

    546: /* --------------------------------------------------------------------------*/

    548: /*MC
    549:    PetscAbs - Returns the absolute value of a number

    551:    Synopsis:
    552: #include <petscmath.h>
    553:    type PetscAbs(type v)

    555:    Not Collective

    557:    Input Parameter:
    558: .  v - the number

    560:    Notes:
    561:     type can be integer or real floating point value

    563:    Level: beginner

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

    567: M*/
    568: #define PetscAbs(a)  (((a) >= 0) ? (a) : (-(a)))

    570: /*MC
    571:    PetscSign - Returns the sign of a number as an integer

    573:    Synopsis:
    574: #include <petscmath.h>
    575:    int PetscSign(type v)

    577:    Not Collective

    579:    Input Parameter:
    580: .  v - the number

    582:    Notes:
    583:     type can be integer or real floating point value

    585:    Level: beginner

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

    590: /*MC
    591:    PetscMin - Returns minimum of two numbers

    593:    Synopsis:
    594: #include <petscmath.h>
    595:    type PetscMin(type v1,type v2)

    597:    Not Collective

    599:    Input Parameters:
    600: +  v1 - first value to find minimum of
    601: -  v2 - second value to find minimum of

    603:    Notes:
    604:     type can be integer or floating point value

    606:    Level: beginner

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

    610: M*/
    611: #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))

    613: /*MC
    614:    PetscMax - Returns maxium of two numbers

    616:    Synopsis:
    617: #include <petscmath.h>
    618:    type max PetscMax(type v1,type v2)

    620:    Not Collective

    622:    Input Parameters:
    623: +  v1 - first value to find maximum of
    624: -  v2 - second value to find maximum of

    626:    Notes:
    627:     type can be integer or floating point value

    629:    Level: beginner

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

    633: M*/
    634: #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))

    636: /*MC
    637:    PetscClipInterval - Returns a number clipped to be within an interval

    639:    Synopsis:
    640: #include <petscmath.h>
    641:    type clip PetscClipInterval(type x,type a,type b)

    643:    Not Collective

    645:    Input Parameters:
    646: +  x - value to use if within interval [a,b]
    647: .  a - lower end of interval
    648: -  b - upper end of interval

    650:    Notes:
    651:     type can be integer or floating point value

    653:    Level: beginner

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

    657: M*/
    658: #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))

    660: /*MC
    661:    PetscAbsInt - Returns the absolute value of an integer

    663:    Synopsis:
    664: #include <petscmath.h>
    665:    int abs PetscAbsInt(int v1)

    667:    Not Collective

    669:    Input Parameter:
    670: .   v1 - the integer

    672:    Level: beginner

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

    676: M*/
    677: #define PetscAbsInt(a)  (((a)<0)   ? (-(a)) : (a))

    679: /*MC
    680:    PetscAbsReal - Returns the absolute value of an real number

    682:    Synopsis:
    683: #include <petscmath.h>
    684:    Real abs PetscAbsReal(PetscReal v1)

    686:    Not Collective

    688:    Input Parameter:
    689: .   v1 - the double

    691:    Level: beginner

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

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

    706: /*MC
    707:    PetscSqr - Returns the square of a number

    709:    Synopsis:
    710: #include <petscmath.h>
    711:    type sqr PetscSqr(type v1)

    713:    Not Collective

    715:    Input Parameter:
    716: .   v1 - the value

    718:    Notes:
    719:     type can be integer or floating point value

    721:    Level: beginner

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

    725: M*/
    726: #define PetscSqr(a)     ((a)*(a))

    728: /* ----------------------------------------------------------------------------*/

    730: #if defined(PETSC_USE_REAL_SINGLE)
    731: #define PetscRealConstant(constant) constant##F
    732: #elif defined(PETSC_USE_REAL_DOUBLE)
    733: #define PetscRealConstant(constant) constant
    734: #elif defined(PETSC_USE_REAL___FLOAT128)
    735: #define PetscRealConstant(constant) constant##Q
    736: #elif defined(PETSC_USE_REAL___FP16)
    737: #define PetscRealConstant(constant) constant##F
    738: #endif

    740: /*
    741:      Basic constants
    742: */
    743: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
    744: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
    745: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

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

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

    782: #define PETSC_INFINITY               (PETSC_MAX_REAL/4)
    783: #define PETSC_NINFINITY              (-PETSC_INFINITY)

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

    794: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
    795: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
    796: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);

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

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

    809: /*
    810:    MPI Datatypes for composite reductions:
    811:    MPIU_REAL_INT -> struct { PetscReal; PetscInt; }
    812:    MPIU_SCALAR_INT -> struct { PetscScalar; PetscInt; }
    813: */
    814: PETSC_EXTERN MPI_Datatype MPIU_REAL_INT;
    815: PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT;

    817: #if defined(PETSC_USE_64BIT_INDICES)
    818: struct petsc_mpiu_2int {PetscInt a,b;};
    819: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
    820: #else
    821: #define MPIU_2INT MPI_2INT
    822: #endif
    823: PETSC_EXTERN MPI_Datatype MPI_4INT;
    824: PETSC_EXTERN MPI_Datatype MPIU_4INT;

    826: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
    827: {
    828:   PetscInt result = 1;
    829:   while (power) {
    830:     if (power & 1) result *= base;
    831:     power >>= 1;
    832:     base *= base;
    833:   }
    834:   return result;
    835: }

    837: PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
    838: {
    839:   PetscInt64 result = 1;
    840:   while (power) {
    841:     if (power & 1) result *= base;
    842:     power >>= 1;
    843:     base *= base;
    844:   }
    845:   return result;
    846: }

    848: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
    849: {
    850:   PetscReal result = 1;
    851:   if (power < 0) {
    852:     power = -power;
    853:     base  = ((PetscReal)1)/base;
    854:   }
    855:   while (power) {
    856:     if (power & 1) result *= base;
    857:     power >>= 1;
    858:     base *= base;
    859:   }
    860:   return result;
    861: }

    863: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
    864: {
    865:   PetscScalar result = (PetscReal)1;
    866:   if (power < 0) {
    867:     power = -power;
    868:     base  = ((PetscReal)1)/base;
    869:   }
    870:   while (power) {
    871:     if (power & 1) result *= base;
    872:     power >>= 1;
    873:     base *= base;
    874:   }
    875:   return result;
    876: }

    878: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
    879: {
    880:   PetscScalar cpower = power;
    881:   return PetscPowScalar(base,cpower);
    882: }

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

    887:    Synopsis:
    888: #include <petscmath.h>
    889:    bool PetscLTE(PetscReal x,constant float)

    891:    Not Collective

    893:    Input Parameters:
    894: +   x - the variable
    895: -   b - the constant float it is checking if x is less than or equal to

    897:    Notes:
    898:      The fudge factor is the value PETSC_SMALL

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

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

    905:    Level: advanced

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

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

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

    915:    Synopsis:
    916: #include <petscmath.h>
    917:    bool PetscGTE(PetscReal x,constant float)

    919:    Not Collective

    921:    Input Parameters:
    922: +   x - the variable
    923: -   b - the constant float it is checking if x is greater than or equal to

    925:    Notes:
    926:      The fudge factor is the value PETSC_SMALL

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

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

    933:    Level: advanced

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

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

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