Date: 2025-03-29T05:58:17+00:00

Actual source code: petscmath.h

      1: /*
      2:     PETSc mathematics include file. Defines certain basic mathematical
      3:     constants and functions for working with single, double, and quad precision
      4:     floating point numbers as well as complex single and double.

      6:     This file is included by petscsys.h and should not be used directly.
      7: */
      8: #pragma once

     10: #include <math.h>
     11: #include <petscmacros.h>
     12: #include <petscsystypes.h>

     14: /* SUBMANSEC = Sys */

     16: /*
     17:    Defines operations that are different for complex and real numbers.
     18:    All PETSc objects in one program are built around the object
     19:    PetscScalar which is either always a real or a complex.
     20: */

     22: /*
     23:     Real number definitions
     24:  */
     25: #if defined(PETSC_USE_REAL_SINGLE)
     26:   #define PetscSqrtReal(a)        sqrtf(a)
     27:   #define PetscCbrtReal(a)        cbrtf(a)
     28:   #define PetscHypotReal(a, b)    hypotf(a, b)
     29:   #define PetscAtan2Real(a, b)    atan2f(a, b)
     30:   #define PetscPowReal(a, b)      powf(a, b)
     31:   #define PetscExpReal(a)         expf(a)
     32:   #define PetscLogReal(a)         logf(a)
     33:   #define PetscLog10Real(a)       log10f(a)
     34:   #define PetscLog2Real(a)        log2f(a)
     35:   #define PetscSinReal(a)         sinf(a)
     36:   #define PetscCosReal(a)         cosf(a)
     37:   #define PetscTanReal(a)         tanf(a)
     38:   #define PetscAsinReal(a)        asinf(a)
     39:   #define PetscAcosReal(a)        acosf(a)
     40:   #define PetscAtanReal(a)        atanf(a)
     41:   #define PetscSinhReal(a)        sinhf(a)
     42:   #define PetscCoshReal(a)        coshf(a)
     43:   #define PetscTanhReal(a)        tanhf(a)
     44:   #define PetscAsinhReal(a)       asinhf(a)
     45:   #define PetscAcoshReal(a)       acoshf(a)
     46:   #define PetscAtanhReal(a)       atanhf(a)
     47:   #define PetscErfReal(a)         erff(a)
     48:   #define PetscCeilReal(a)        ceilf(a)
     49:   #define PetscFloorReal(a)       floorf(a)
     50:   #define PetscRintReal(a)        rintf(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 PetscErfReal(a)         erf(a)
     83:   #define PetscCeilReal(a)        ceil(a)
     84:   #define PetscFloorReal(a)       floor(a)
     85:   #define PetscRintReal(a)        rint(a)
     86:   #define PetscFmodReal(a, b)     fmod(a, b)
     87:   #define PetscCopysignReal(a, b) copysign(a, b)
     88:   #define PetscTGamma(a)          tgamma(a)
     89:   #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
     90:     #define PetscLGamma(a) gamma(a)
     91:   #else
     92:     #define PetscLGamma(a) lgamma(a)
     93:   #endif

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

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

    165: #endif /* PETSC_USE_REAL_* */

    167: static inline PetscReal PetscSignReal(PetscReal a)
    168: {
    169:   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
    170: }

    172: #if !defined(PETSC_HAVE_LOG2)
    173:   #undef PetscLog2Real
    174: static inline PetscReal PetscLog2Real(PetscReal a)
    175: {
    176:   return PetscLogReal(a) / PetscLogReal((PetscReal)2);
    177: }
    178: #endif

    180: #if defined(PETSC_HAVE_REAL___FLOAT128) && !defined(PETSC_SKIP_REAL___FLOAT128)
    181: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__float128);
    182: #endif
    183: #if defined(PETSC_HAVE_REAL___FP16) && !defined(PETSC_SKIP_REAL___FP16)
    184: PETSC_EXTERN MPI_Datatype MPIU___FP16 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__fp16);
    185: #endif

    187: /*MC
    188:    MPIU_REAL - Portable MPI datatype corresponding to `PetscReal` independent of what precision `PetscReal` is in

    190:    Level: beginner

    192:    Note:
    193:    In MPI calls that require an MPI datatype that matches a `PetscReal` or array of `PetscReal` values, pass this value.

    195: .seealso: `PetscReal`, `PetscScalar`, `PetscComplex`, `PetscInt`, `MPIU_SCALAR`, `MPIU_COMPLEX`, `MPIU_INT`
    196: M*/
    197: #if defined(PETSC_USE_REAL_SINGLE)
    198:   #define MPIU_REAL MPI_FLOAT
    199: #elif defined(PETSC_USE_REAL_DOUBLE)
    200:   #define MPIU_REAL MPI_DOUBLE
    201: #elif defined(PETSC_USE_REAL___FLOAT128)
    202:   #define MPIU_REAL MPIU___FLOAT128
    203: #elif defined(PETSC_USE_REAL___FP16)
    204:   #define MPIU_REAL MPIU___FP16
    205: #endif /* PETSC_USE_REAL_* */

    207: /*
    208:     Complex number definitions
    209:  */
    210: #if defined(PETSC_HAVE_COMPLEX)
    211:   #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
    212:   /* C++ support of complex number */

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

    236:   /* TODO: Add configure tests

    238: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
    239: #undef PetscTanComplex
    240: static inline PetscComplex PetscTanComplex(PetscComplex z)
    241: {
    242:   return PetscSinComplex(z)/PetscCosComplex(z);
    243: }
    244: #endif

    246: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
    247: #undef PetscTanhComplex
    248: static inline PetscComplex PetscTanhComplex(PetscComplex z)
    249: {
    250:   return PetscSinhComplex(z)/PetscCoshComplex(z);
    251: }
    252: #endif

    254: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
    255: #undef PetscAsinComplex
    256: static inline PetscComplex PetscAsinComplex(PetscComplex z)
    257: {
    258:   const PetscComplex j(0,1);
    259:   return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
    260: }
    261: #endif

    263: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
    264: #undef PetscAcosComplex
    265: static inline PetscComplex PetscAcosComplex(PetscComplex z)
    266: {
    267:   const PetscComplex j(0,1);
    268:   return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
    269: }
    270: #endif

    272: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
    273: #undef PetscAtanComplex
    274: static inline PetscComplex PetscAtanComplex(PetscComplex z)
    275: {
    276:   const PetscComplex j(0,1);
    277:   return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
    278: }
    279: #endif

    281: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
    282: #undef PetscAsinhComplex
    283: static inline PetscComplex PetscAsinhComplex(PetscComplex z)
    284: {
    285:   return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
    286: }
    287: #endif

    289: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
    290: #undef PetscAcoshComplex
    291: static inline PetscComplex PetscAcoshComplex(PetscComplex z)
    292: {
    293:   return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
    294: }
    295: #endif

    297: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
    298: #undef PetscAtanhComplex
    299: static inline PetscComplex PetscAtanhComplex(PetscComplex z)
    300: {
    301:   return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
    302: }
    303: #endif

    305: */

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

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

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

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

    378:     #endif /* PETSC_USE_REAL_* */
    379:   #endif   /* (__cplusplus) */

    381: /*MC
    382:    PETSC_i - the pure imaginary complex number i

    384:    Level: intermediate

    386: .seealso: `PetscComplex`, `PetscScalar`
    387: M*/
    388: PETSC_EXTERN PetscComplex PETSC_i;

    390: /*
    391:    Try to do the right thing for complex number construction: see
    392:    http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
    393:    for details
    394: */
    395: static inline PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
    396: {
    397:   #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
    398:   return PetscComplex(x, y);
    399:   #elif defined(_Imaginary_I)
    400:   return x + y * _Imaginary_I;
    401:   #else
    402:   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),

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

    408:        So type punning should be portable. */
    409:     union
    410:     {
    411:       PetscComplex z;
    412:       PetscReal    f[2];
    413:     } uz;

    415:     uz.f[0] = x;
    416:     uz.f[1] = y;
    417:     return uz.z;
    418:   }
    419:   #endif
    420: }

    422:   #define MPIU_C_COMPLEX        MPI_C_COMPLEX PETSC_DEPRECATED_MACRO(3, 15, 0, "MPI_C_COMPLEX", )
    423:   #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX PETSC_DEPRECATED_MACRO(3, 15, 0, "MPI_C_DOUBLE_COMPLEX", )

    425:   #if defined(PETSC_HAVE_REAL___FLOAT128) && !defined(PETSC_SKIP_REAL___FLOAT128)
    426:     // if complex is not used, then quadmath.h won't be included by petscsystypes.h
    427:     #if defined(PETSC_USE_COMPLEX)
    428:       #define MPIU___COMPLEX128_ATTR_TAG PETSC_ATTRIBUTE_MPI_TYPE_TAG(__complex128)
    429:     #else
    430:       #define MPIU___COMPLEX128_ATTR_TAG
    431:     #endif

    433: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 MPIU___COMPLEX128_ATTR_TAG;

    435:     #undef MPIU___COMPLEX128_ATTR_TAG
    436:   #endif /* PETSC_HAVE_REAL___FLOAT128 */

    438:   /*MC
    439:    MPIU_COMPLEX - Portable MPI datatype corresponding to `PetscComplex` independent of the precision of `PetscComplex`

    441:    Level: beginner

    443:    Note:
    444:    In MPI calls that require an MPI datatype that matches a `PetscComplex` or array of `PetscComplex` values, pass this value.

    446: .seealso: `PetscReal`, `PetscScalar`, `PetscComplex`, `PetscInt`, `MPIU_REAL`, `MPIU_SCALAR`, `MPIU_COMPLEX`, `MPIU_INT`, `PETSC_i`
    447: M*/
    448:   #if defined(PETSC_USE_REAL_SINGLE)
    449:     #define MPIU_COMPLEX MPI_C_COMPLEX
    450:   #elif defined(PETSC_USE_REAL_DOUBLE)
    451:     #define MPIU_COMPLEX MPI_C_DOUBLE_COMPLEX
    452:   #elif defined(PETSC_USE_REAL___FLOAT128)
    453:     #define MPIU_COMPLEX MPIU___COMPLEX128
    454:   #elif defined(PETSC_USE_REAL___FP16)
    455:     #define MPIU_COMPLEX MPI_C_COMPLEX
    456:   #endif /* PETSC_USE_REAL_* */

    458: #endif /* PETSC_HAVE_COMPLEX */

    460: /*
    461:     Scalar number definitions
    462:  */
    463: #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
    464:   /*MC
    465:    MPIU_SCALAR - Portable MPI datatype corresponding to `PetscScalar` independent of the precision of `PetscScalar`

    467:    Level: beginner

    469:    Note:
    470:    In MPI calls that require an MPI datatype that matches a `PetscScalar` or array of `PetscScalar` values, pass this value.

    472: .seealso: `PetscReal`, `PetscScalar`, `PetscComplex`, `PetscInt`, `MPIU_REAL`, `MPIU_COMPLEX`, `MPIU_INT`
    473: M*/
    474:   #define MPIU_SCALAR MPIU_COMPLEX

    476:   /*MC
    477:    PetscRealPart - Returns the real part of a `PetscScalar`

    479:    Synopsis:
    480: #include <petscmath.h>
    481:    PetscReal PetscRealPart(PetscScalar v)

    483:    Not Collective

    485:    Input Parameter:
    486: .  v - value to find the real part of

    488:    Level: beginner

    490: .seealso: `PetscScalar`, `PetscImaginaryPart()`, `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    491: M*/
    492:   #define PetscRealPart(a) PetscRealPartComplex(a)

    494:   /*MC
    495:    PetscImaginaryPart - Returns the imaginary part of a `PetscScalar`

    497:    Synopsis:
    498: #include <petscmath.h>
    499:    PetscReal PetscImaginaryPart(PetscScalar v)

    501:    Not Collective

    503:    Input Parameter:
    504: .  v - value to find the imaginary part of

    506:    Level: beginner

    508:    Note:
    509:    If PETSc was configured for real numbers then this always returns the value 0

    511: .seealso: `PetscScalar`, `PetscRealPart()`, `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    512: M*/
    513:   #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

    515:   #define PetscAbsScalar(a)    PetscAbsComplex(a)
    516:   #define PetscArgScalar(a)    PetscArgComplex(a)
    517:   #define PetscConj(a)         PetscConjComplex(a)
    518:   #define PetscSqrtScalar(a)   PetscSqrtComplex(a)
    519:   #define PetscPowScalar(a, b) PetscPowComplex(a, b)
    520:   #define PetscExpScalar(a)    PetscExpComplex(a)
    521:   #define PetscLogScalar(a)    PetscLogComplex(a)
    522:   #define PetscSinScalar(a)    PetscSinComplex(a)
    523:   #define PetscCosScalar(a)    PetscCosComplex(a)
    524:   #define PetscTanScalar(a)    PetscTanComplex(a)
    525:   #define PetscAsinScalar(a)   PetscAsinComplex(a)
    526:   #define PetscAcosScalar(a)   PetscAcosComplex(a)
    527:   #define PetscAtanScalar(a)   PetscAtanComplex(a)
    528:   #define PetscSinhScalar(a)   PetscSinhComplex(a)
    529:   #define PetscCoshScalar(a)   PetscCoshComplex(a)
    530:   #define PetscTanhScalar(a)   PetscTanhComplex(a)
    531:   #define PetscAsinhScalar(a)  PetscAsinhComplex(a)
    532:   #define PetscAcoshScalar(a)  PetscAcoshComplex(a)
    533:   #define PetscAtanhScalar(a)  PetscAtanhComplex(a)

    535: #else /* PETSC_USE_COMPLEX */
    536:   #define MPIU_SCALAR           MPIU_REAL
    537:   #define PetscRealPart(a)      (a)
    538:   #define PetscImaginaryPart(a) ((PetscReal)0)
    539:   #define PetscAbsScalar(a)     PetscAbsReal(a)
    540:   #define PetscArgScalar(a)     (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
    541:   #define PetscConj(a)          (a)
    542:   #define PetscSqrtScalar(a)    PetscSqrtReal(a)
    543:   #define PetscPowScalar(a, b)  PetscPowReal(a, b)
    544:   #define PetscExpScalar(a)     PetscExpReal(a)
    545:   #define PetscLogScalar(a)     PetscLogReal(a)
    546:   #define PetscSinScalar(a)     PetscSinReal(a)
    547:   #define PetscCosScalar(a)     PetscCosReal(a)
    548:   #define PetscTanScalar(a)     PetscTanReal(a)
    549:   #define PetscAsinScalar(a)    PetscAsinReal(a)
    550:   #define PetscAcosScalar(a)    PetscAcosReal(a)
    551:   #define PetscAtanScalar(a)    PetscAtanReal(a)
    552:   #define PetscSinhScalar(a)    PetscSinhReal(a)
    553:   #define PetscCoshScalar(a)    PetscCoshReal(a)
    554:   #define PetscTanhScalar(a)    PetscTanhReal(a)
    555:   #define PetscAsinhScalar(a)   PetscAsinhReal(a)
    556:   #define PetscAcoshScalar(a)   PetscAcoshReal(a)
    557:   #define PetscAtanhScalar(a)   PetscAtanhReal(a)

    559: #endif /* PETSC_USE_COMPLEX */

    561: /*
    562:    Certain objects may be created using either single or double precision.
    563:    This is currently not used.
    564: */
    565: typedef enum {
    566:   PETSC_SCALAR_DOUBLE,
    567:   PETSC_SCALAR_SINGLE,
    568:   PETSC_SCALAR_LONG_DOUBLE,
    569:   PETSC_SCALAR_HALF
    570: } PetscScalarPrecision;

    572: /*MC
    573:    PetscAbs - Returns the absolute value of a number

    575:    Synopsis:
    576: #include <petscmath.h>
    577:    type PetscAbs(type v)

    579:    Not Collective

    581:    Input Parameter:
    582: .  v - the number

    584:    Level: beginner

    586:    Note:
    587:    The type can be integer or real floating point value, but cannot be complex

    589: .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()`, `PetscSign()`
    590: M*/
    591: #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a)))

    593: /*MC
    594:    PetscSign - Returns the sign of a number as an integer of value -1, 0, or 1

    596:    Synopsis:
    597: #include <petscmath.h>
    598:    int PetscSign(type v)

    600:    Not Collective

    602:    Input Parameter:
    603: .  v - the number

    605:    Level: beginner

    607:    Note:
    608:    The type can be integer or real floating point value

    610: .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()`
    611: M*/
    612: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)

    614: /*MC
    615:    PetscMin - Returns minimum of two numbers

    617:    Synopsis:
    618: #include <petscmath.h>
    619:    type PetscMin(type v1,type v2)

    621:    Not Collective

    623:    Input Parameters:
    624: +  v1 - first value to find minimum of
    625: -  v2 - second value to find minimum of

    627:    Level: beginner

    629:    Note:
    630:    The type can be integer or floating point value, but cannot be complex

    632: .seealso: `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    633: M*/
    634: #define PetscMin(a, b) (((a) < (b)) ? (a) : (b))

    636: /*MC
    637:    PetscMax - Returns maximum of two numbers

    639:    Synopsis:
    640: #include <petscmath.h>
    641:    type max PetscMax(type v1,type v2)

    643:    Not Collective

    645:    Input Parameters:
    646: +  v1 - first value to find maximum of
    647: -  v2 - second value to find maximum of

    649:    Level: beginner

    651:    Note:
    652:    The type can be integer or floating point value

    654: .seealso: `PetscMin()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    655: M*/
    656: #define PetscMax(a, b) (((a) < (b)) ? (b) : (a))

    658: /*MC
    659:    PetscClipInterval - Returns a number clipped to be within an interval

    661:    Synopsis:
    662: #include <petscmath.h>
    663:    type clip PetscClipInterval(type x,type a,type b)

    665:    Not Collective

    667:    Input Parameters:
    668: +  x - value to use if within interval [a,b]
    669: .  a - lower end of interval
    670: -  b - upper end of interval

    672:    Level: beginner

    674:    Note:
    675:    The type can be integer or floating point value

    677:    Example\:
    678: .vb
    679:   PetscInt c = PetscClipInterval(5, 2, 3); // the value of c is 3
    680:   PetscInt c = PetscClipInterval(5, 2, 6); // the value of c is 5
    681: .ve

    683: .seealso: `PetscMin()`, `PetscMax()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    684: M*/
    685: #define PetscClipInterval(x, a, b) (PetscMax((a), PetscMin((x), (b))))

    687: /*MC
    688:    PetscAbsInt - Returns the absolute value of an integer

    690:    Synopsis:
    691: #include <petscmath.h>
    692:    int abs PetscAbsInt(int v1)

    694:    Input Parameter:
    695: .   v1 - the integer

    697:    Level: beginner

    699: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsReal()`, `PetscSqr()`
    700: M*/
    701: #define PetscAbsInt(a) (((a) < 0) ? (-(a)) : (a))

    703: /*MC
    704:    PetscAbsReal - Returns the absolute value of a real number

    706:    Synopsis:
    707: #include <petscmath.h>
    708:    Real abs PetscAbsReal(PetscReal v1)

    710:    Input Parameter:
    711: .   v1 - the `PetscReal` value

    713:    Level: beginner

    715: .seealso: `PetscReal`, `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscSqr()`
    716: M*/
    717: #if defined(PETSC_USE_REAL_SINGLE)
    718:   #define PetscAbsReal(a) fabsf(a)
    719: #elif defined(PETSC_USE_REAL_DOUBLE)
    720:   #define PetscAbsReal(a) fabs(a)
    721: #elif defined(PETSC_USE_REAL___FLOAT128)
    722:   #define PetscAbsReal(a) fabsq(a)
    723: #elif defined(PETSC_USE_REAL___FP16)
    724:   #define PetscAbsReal(a) fabsf(a)
    725: #endif

    727: /*MC
    728:    PetscSqr - Returns the square of a number

    730:    Synopsis:
    731: #include <petscmath.h>
    732:    type sqr PetscSqr(type v1)

    734:    Not Collective

    736:    Input Parameter:
    737: .   v1 - the value

    739:    Level: beginner

    741:    Note:
    742:    The type can be integer, floating point, or complex floating point

    744: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`
    745: M*/
    746: #define PetscSqr(a) ((a) * (a))

    748: /*MC
    749:    PetscRealConstant - a compile time macro that ensures a given constant real number is properly represented in the configured
    750:    precision of `PetscReal` be it half, single, double or 128-bit representation

    752:    Synopsis:
    753: #include <petscmath.h>
    754:    PetscReal PetscRealConstant(real_number)

    756:    Not Collective

    758:    Input Parameter:
    759: .   v1 - the real number, for example 1.5

    761:    Level: beginner

    763:    Note:
    764:    For example, if PETSc is configured with `--with-precision=__float128` and one writes
    765: .vb
    766:    PetscReal d = 1.5;
    767: .ve
    768:    the result is 1.5 in double precision extended to 128 bit representation, meaning it is very far from the correct value. Hence, one should write
    769: .vb
    770:    PetscReal d = PetscRealConstant(1.5);
    771: .ve

    773: .seealso: `PetscReal`
    774: M*/
    775: #if defined(PETSC_USE_REAL_SINGLE)
    776:   #define PetscRealConstant(constant) constant##F
    777: #elif defined(PETSC_USE_REAL_DOUBLE)
    778:   #define PetscRealConstant(constant) constant
    779: #elif defined(PETSC_USE_REAL___FLOAT128)
    780:   #define PetscRealConstant(constant) constant##Q
    781: #elif defined(PETSC_USE_REAL___FP16)
    782:   #define PetscRealConstant(constant) constant##F
    783: #endif

    785: /*
    786:      Basic constants
    787: */
    788: /*MC
    789:   PETSC_PI - the value of $ \pi$ to the correct precision of `PetscReal`.

    791:   Level: beginner

    793: .seealso: `PetscReal`, `PETSC_PHI`, `PETSC_SQRT2`
    794: M*/

    796: /*MC
    797:   PETSC_PHI - the value of $ \phi$, the Golden Ratio, to the correct precision of `PetscReal`.

    799:   Level: beginner

    801: .seealso: `PetscReal`, `PETSC_PI`, `PETSC_SQRT2`
    802: M*/

    804: /*MC
    805:   PETSC_SQRT2 - the value of $ \sqrt{2} $ to the correct precision of `PetscReal`.

    807:   Level: beginner

    809: .seealso: `PetscReal`, `PETSC_PI`, `PETSC_PHI`
    810: M*/

    812: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
    813: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
    814: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

    816: /*MC
    817:   PETSC_MAX_REAL - the largest real value that can be stored in a `PetscReal`

    819:   Level: beginner

    821: .seealso: `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    822: M*/

    824: /*MC
    825:   PETSC_MIN_REAL - the smallest real value that can be stored in a `PetscReal`, generally this is - `PETSC_MAX_REAL`

    827:   Level: beginner

    829: .seealso `PETSC_MAX_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    830: M*/

    832: /*MC
    833:   PETSC_REAL_MIN - the smallest positive normalized real value that can be stored in a `PetscReal`.

    835:   Level: beginner

    837:   Note:
    838:   See <https://en.wikipedia.org/wiki/Subnormal_number> for a discussion of normalized and subnormal floating point numbers

    840:   Developer Note:
    841:   The naming is confusing as there is both a `PETSC_REAL_MIN` and `PETSC_MIN_REAL` with different meanings.

    843: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    844: M*/

    846: /*MC
    847:   PETSC_MACHINE_EPSILON - the machine epsilon for the precision of `PetscReal`

    849:   Level: beginner

    851:   Note:
    852:   See <https://en.wikipedia.org/wiki/Machine_epsilon>

    854: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    855: M*/

    857: /*MC
    858:   PETSC_SQRT_MACHINE_EPSILON - the square root of the machine epsilon for the precision of `PetscReal`

    860:   Level: beginner

    862:   Note:
    863:   See `PETSC_MACHINE_EPSILON`

    865: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SMALL`
    866: M*/

    868: /*MC
    869:   PETSC_SMALL - an arbitrary "small" number which depends on the precision of `PetscReal` used in some PETSc examples
    870:   and in `PetscApproximateLTE()` and `PetscApproximateGTE()` to determine if a computation was successful.

    872:   Level: beginner

    874:   Note:
    875:   See `PETSC_MACHINE_EPSILON`

    877: .seealso `PetscApproximateLTE()`, `PetscApproximateGTE()`, `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`,
    878:          `PETSC_SQRT_MACHINE_EPSILON`
    879: M*/

    881: #if defined(PETSC_USE_REAL_SINGLE)
    882:   #define PETSC_MAX_REAL             3.40282346638528860e+38F
    883:   #define PETSC_MIN_REAL             (-PETSC_MAX_REAL)
    884:   #define PETSC_REAL_MIN             1.1754944e-38F
    885:   #define PETSC_MACHINE_EPSILON      1.19209290e-07F
    886:   #define PETSC_SQRT_MACHINE_EPSILON 3.45266983e-04F
    887:   #define PETSC_SMALL                1.e-5F
    888: #elif defined(PETSC_USE_REAL_DOUBLE)
    889:   #define PETSC_MAX_REAL             1.7976931348623157e+308
    890:   #define PETSC_MIN_REAL             (-PETSC_MAX_REAL)
    891:   #define PETSC_REAL_MIN             2.225073858507201e-308
    892:   #define PETSC_MACHINE_EPSILON      2.2204460492503131e-16
    893:   #define PETSC_SQRT_MACHINE_EPSILON 1.490116119384766e-08
    894:   #define PETSC_SMALL                1.e-10
    895: #elif defined(PETSC_USE_REAL___FLOAT128)
    896:   #define PETSC_MAX_REAL             FLT128_MAX
    897:   #define PETSC_MIN_REAL             (-FLT128_MAX)
    898:   #define PETSC_REAL_MIN             FLT128_MIN
    899:   #define PETSC_MACHINE_EPSILON      FLT128_EPSILON
    900:   #define PETSC_SQRT_MACHINE_EPSILON 1.38777878078144567552953958511352539e-17Q
    901:   #define PETSC_SMALL                1.e-20Q
    902: #elif defined(PETSC_USE_REAL___FP16)
    903:   #define PETSC_MAX_REAL             65504.0F
    904:   #define PETSC_MIN_REAL             (-PETSC_MAX_REAL)
    905:   #define PETSC_REAL_MIN             .00006103515625F
    906:   #define PETSC_MACHINE_EPSILON      .0009765625F
    907:   #define PETSC_SQRT_MACHINE_EPSILON .03125F
    908:   #define PETSC_SMALL                5.e-3F
    909: #endif

    911: /*MC
    912:   PETSC_INFINITY - a finite number that represents infinity for setting certain bounds in `Tao`

    914:   Level: intermediate

    916:   Note:
    917:   This is not the IEEE infinity value

    919: .seealso: `PETSC_NINFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()`
    920: M*/
    921: #define PETSC_INFINITY (PETSC_MAX_REAL / 4)

    923: /*MC
    924:   PETSC_NINFINITY - a finite number that represents negative infinity for setting certain bounds in `Tao`

    926:   Level: intermediate

    928:   Note:
    929:   This is not the negative IEEE infinity value

    931: .seealso: `PETSC_INFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()`
    932: M*/
    933: #define PETSC_NINFINITY (-PETSC_INFINITY)

    935: PETSC_EXTERN PetscBool  PetscIsInfReal(PetscReal);
    936: PETSC_EXTERN PetscBool  PetscIsNanReal(PetscReal);
    937: PETSC_EXTERN PetscBool  PetscIsNormalReal(PetscReal);
    938: static inline PetscBool PetscIsInfOrNanReal(PetscReal v)
    939: {
    940:   return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;
    941: }
    942: static inline PetscBool PetscIsInfScalar(PetscScalar v)
    943: {
    944:   return PetscIsInfReal(PetscAbsScalar(v));
    945: }
    946: static inline PetscBool PetscIsNanScalar(PetscScalar v)
    947: {
    948:   return PetscIsNanReal(PetscAbsScalar(v));
    949: }
    950: static inline PetscBool PetscIsInfOrNanScalar(PetscScalar v)
    951: {
    952:   return PetscIsInfOrNanReal(PetscAbsScalar(v));
    953: }
    954: static inline PetscBool PetscIsNormalScalar(PetscScalar v)
    955: {
    956:   return PetscIsNormalReal(PetscAbsScalar(v));
    957: }

    959: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal, PetscReal, PetscReal, PetscReal);
    960: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal, PetscReal);
    961: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar, PetscScalar);

    963: /*@C
    964:   PetscIsCloseAtTolScalar - Like `PetscIsCloseAtTol()` but for `PetscScalar`

    966:   Input Parameters:
    967: + lhs  - The first number
    968: . rhs  - The second number
    969: . rtol - The relative tolerance
    970: - atol - The absolute tolerance

    972:   Level: beginner

    974:   Note:
    975:   This routine is equivalent to `PetscIsCloseAtTol()` when PETSc is configured without complex
    976:   numbers.

    978: .seealso: `PetscIsCloseAtTol()`
    979: @*/
    980: static inline PetscBool PetscIsCloseAtTolScalar(PetscScalar lhs, PetscScalar rhs, PetscReal rtol, PetscReal atol)
    981: {
    982:   PetscBool close = PetscIsCloseAtTol(PetscRealPart(lhs), PetscRealPart(rhs), rtol, atol);

    984:   if (PetscDefined(USE_COMPLEX)) close = (PetscBool)(close && PetscIsCloseAtTol(PetscImaginaryPart(lhs), PetscImaginaryPart(rhs), rtol, atol));
    985:   return close;
    986: }

    988: /*
    989:     These macros are currently hardwired to match the regular data types, so there is no support for a different
    990:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
    991:  */
    992: #define MPIU_MATSCALAR MPIU_SCALAR
    993: typedef PetscScalar MatScalar;
    994: typedef PetscReal   MatReal;

    996: struct petsc_mpiu_2scalar {
    997:   PetscScalar a, b;
    998: };
    999: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2scalar);

    1001: /* MPI Datatypes for composite reductions */
    1002: struct petsc_mpiu_real_int {
    1003:   PetscReal v;
    1004:   PetscInt  i;
    1005: };

    1007: struct petsc_mpiu_scalar_int {
    1008:   PetscScalar v;
    1009:   PetscInt    i;
    1010: };

    1012: PETSC_EXTERN MPI_Datatype MPIU_REAL_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_real_int);
    1013: PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_scalar_int);

    1015: #if defined(PETSC_USE_64BIT_INDICES)
    1016: struct /* __attribute__((packed, aligned(alignof(PetscInt *)))) */ petsc_mpiu_2int {
    1017:   PetscInt a;
    1018:   PetscInt b;
    1019: };
    1020: struct __attribute__((packed)) petsc_mpiu_int_mpiint {
    1021:   PetscInt    a;
    1022:   PetscMPIInt b;
    1023: };
    1024: /*
    1025:  static_assert(sizeof(struct petsc_mpiu_2int) == 2 * sizeof(PetscInt), "");
    1026:  static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt *), "");
    1027:  static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt[2]), "");

    1029:  clang generates warnings that petsc_mpiu_2int is not layout compatible with PetscInt[2] or
    1030:  PetscInt *, even though (with everything else uncommented) both of the static_asserts above
    1031:  pass! So we just comment it out...
    1032: */
    1033: PETSC_EXTERN MPI_Datatype MPIU_2INT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2int) */;
    1034: PETSC_EXTERN MPI_Datatype MPIU_INT_MPIINT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_int_mpiint) */;
    1035: #else
    1036:   #define MPIU_2INT       MPI_2INT
    1037:   #define MPIU_INT_MPIINT MPI_2INT
    1038: #endif
    1039: PETSC_EXTERN MPI_Datatype MPI_4INT;
    1040: PETSC_EXTERN MPI_Datatype MPIU_4INT;

    1042: static inline PetscInt PetscPowInt(PetscInt base, PetscInt power)
    1043: {
    1044:   PetscInt result = 1;
    1045:   while (power) {
    1046:     if (power & 1) result *= base;
    1047:     power >>= 1;
    1048:     if (power) base *= base;
    1049:   }
    1050:   return result;
    1051: }

    1053: static inline PetscInt64 PetscPowInt64(PetscInt base, PetscInt power)
    1054: {
    1055:   PetscInt64 result = 1;
    1056:   while (power) {
    1057:     if (power & 1) result *= base;
    1058:     power >>= 1;
    1059:     if (power) base *= base;
    1060:   }
    1061:   return result;
    1062: }

    1064: static inline PetscReal PetscPowRealInt(PetscReal base, PetscInt power)
    1065: {
    1066:   PetscReal result = 1;
    1067:   if (power < 0) {
    1068:     power = -power;
    1069:     base  = ((PetscReal)1) / base;
    1070:   }
    1071:   while (power) {
    1072:     if (power & 1) result *= base;
    1073:     power >>= 1;
    1074:     if (power) base *= base;
    1075:   }
    1076:   return result;
    1077: }

    1079: static inline PetscScalar PetscPowScalarInt(PetscScalar base, PetscInt power)
    1080: {
    1081:   PetscScalar result = (PetscReal)1;
    1082:   if (power < 0) {
    1083:     power = -power;
    1084:     base  = ((PetscReal)1) / base;
    1085:   }
    1086:   while (power) {
    1087:     if (power & 1) result *= base;
    1088:     power >>= 1;
    1089:     if (power) base *= base;
    1090:   }
    1091:   return result;
    1092: }

    1094: static inline PetscScalar PetscPowScalarReal(PetscScalar base, PetscReal power)
    1095: {
    1096:   PetscScalar cpower = power;
    1097:   return PetscPowScalar(base, cpower);
    1098: }

    1100: /*MC
    1101:    PetscApproximateLTE - Performs a less than or equal to on a given constant with a fudge for floating point numbers

    1103:    Synopsis:
    1104: #include <petscmath.h>
    1105:    bool PetscApproximateLTE(PetscReal x,constant float)

    1107:    Not Collective

    1109:    Input Parameters:
    1110: +   x - the variable
    1111: -   b - the constant float it is checking if `x` is less than or equal to

    1113:    Level: advanced

    1115:    Notes:
    1116:    The fudge factor is the value `PETSC_SMALL`

    1118:    The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    1120:    This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    1121:    floating point results.

    1123:    Example\:
    1124: .vb
    1125:   PetscReal x;
    1126:   if (PetscApproximateLTE(x, 3.2)) { // replaces if (x <= 3.2) {
    1127: .ve

    1129: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateGTE()`
    1130: M*/
    1131: #define PetscApproximateLTE(x, b) ((x) <= (PetscRealConstant(b) + PETSC_SMALL))

    1133: /*MC
    1134:    PetscApproximateGTE - Performs a greater than or equal to on a given constant with a fudge for floating point numbers

    1136:    Synopsis:
    1137: #include <petscmath.h>
    1138:    bool PetscApproximateGTE(PetscReal x,constant float)

    1140:    Not Collective

    1142:    Input Parameters:
    1143: +   x - the variable
    1144: -   b - the constant float it is checking if `x` is greater than or equal to

    1146:    Level: advanced

    1148:    Notes:
    1149:    The fudge factor is the value `PETSC_SMALL`

    1151:    The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    1153:    This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    1154:    floating point results.

    1156:    Example\:
    1157: .vb
    1158:   PetscReal x;
    1159:   if (PetscApproximateGTE(x, 3.2)) {  // replaces if (x >= 3.2) {
    1160: .ve

    1162: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()`
    1163: M*/
    1164: #define PetscApproximateGTE(x, b) ((x) >= (PetscRealConstant(b) - PETSC_SMALL))

    1166: /*@C
    1167:    PetscCeilInt - Returns the ceiling of the quotation of two positive integers

    1169:    Not Collective

    1171:    Input Parameters:
    1172: +   x - the numerator
    1173: -   y - the denominator

    1175:    Level: advanced

    1177:   Example\:
    1178: .vb
    1179:   PetscInt n = PetscCeilInt(10, 3); // n has the value of 4
    1180: .ve

    1182: .seealso: `PetscCeilInt64()`, `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()`
    1183: @*/
    1184: static inline PetscInt PetscCeilInt(PetscInt x, PetscInt y)
    1185: {
    1186:   return x / y + (x % y ? 1 : 0);
    1187: }

    1189: /*@C
    1190:    PetscCeilInt64 - Returns the ceiling of the quotation of two positive integers

    1192:    Not Collective

    1194:    Input Parameters:
    1195: +   x - the numerator
    1196: -   y - the denominator

    1198:    Level: advanced

    1200:   Example\:
    1201: .vb
    1202:   PetscInt64 n = PetscCeilInt64(10, 3); // n has the value of 4
    1203: .ve

    1205: .seealso: `PetscCeilInt()`, `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()`
    1206: @*/
    1207: static inline PetscInt64 PetscCeilInt64(PetscInt64 x, PetscInt64 y)
    1208: {
    1209:   return x / y + (x % y ? 1 : 0);
    1210: }

    1212: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt, const PetscReal[], const PetscReal[], PetscReal *, PetscReal *);