Date: 2025-03-28T21:10:40+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 PetscFmodReal(a, b)     fmodf(a, b)
     51:   #define PetscCopysignReal(a, b) copysignf(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 PetscErfReal(a)         erf(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 PetscErfReal(a)         erfq(a)
    116:   #define PetscCeilReal(a)        ceilq(a)
    117:   #define PetscFloorReal(a)       floorq(a)
    118:   #define PetscFmodReal(a, b)     fmodq(a, b)
    119:   #define PetscCopysignReal(a, b) copysignq(a, b)
    120:   #define PetscTGamma(a)          tgammaq(a)
    121:   #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
    122:     #define PetscLGamma(a) gammaq(a)
    123:   #else
    124:     #define PetscLGamma(a) lgammaq(a)
    125:   #endif

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

    161: #endif /* PETSC_USE_REAL_* */

    163: static inline PetscReal PetscSignReal(PetscReal a)
    164: {
    165:   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
    166: }

    168: #if !defined(PETSC_HAVE_LOG2)
    169:   #undef PetscLog2Real
    170: static inline PetscReal PetscLog2Real(PetscReal a)
    171: {
    172:   return PetscLogReal(a) / PetscLogReal((PetscReal)2);
    173: }
    174: #endif

    176: #if defined(PETSC_HAVE_REAL___FLOAT128) && !defined(PETSC_SKIP_REAL___FLOAT128)
    177: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__float128);
    178: #endif
    179: #if defined(PETSC_HAVE_REAL___FP16) && !defined(PETSC_SKIP_REAL___FP16)
    180: PETSC_EXTERN MPI_Datatype MPIU___FP16 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__fp16);
    181: #endif

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

    186:    Level: beginner

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

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

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

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

    232:   /* TODO: Add configure tests

    234: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
    235: #undef PetscTanComplex
    236: static inline PetscComplex PetscTanComplex(PetscComplex z)
    237: {
    238:   return PetscSinComplex(z)/PetscCosComplex(z);
    239: }
    240: #endif

    242: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
    243: #undef PetscTanhComplex
    244: static inline PetscComplex PetscTanhComplex(PetscComplex z)
    245: {
    246:   return PetscSinhComplex(z)/PetscCoshComplex(z);
    247: }
    248: #endif

    250: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
    251: #undef PetscAsinComplex
    252: static inline PetscComplex PetscAsinComplex(PetscComplex z)
    253: {
    254:   const PetscComplex j(0,1);
    255:   return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
    256: }
    257: #endif

    259: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
    260: #undef PetscAcosComplex
    261: static inline PetscComplex PetscAcosComplex(PetscComplex z)
    262: {
    263:   const PetscComplex j(0,1);
    264:   return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
    265: }
    266: #endif

    268: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
    269: #undef PetscAtanComplex
    270: static inline PetscComplex PetscAtanComplex(PetscComplex z)
    271: {
    272:   const PetscComplex j(0,1);
    273:   return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
    274: }
    275: #endif

    277: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
    278: #undef PetscAsinhComplex
    279: static inline PetscComplex PetscAsinhComplex(PetscComplex z)
    280: {
    281:   return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
    282: }
    283: #endif

    285: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
    286: #undef PetscAcoshComplex
    287: static inline PetscComplex PetscAcoshComplex(PetscComplex z)
    288: {
    289:   return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
    290: }
    291: #endif

    293: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
    294: #undef PetscAtanhComplex
    295: static inline PetscComplex PetscAtanhComplex(PetscComplex z)
    296: {
    297:   return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
    298: }
    299: #endif

    301: */

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

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

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

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

    374:     #endif /* PETSC_USE_REAL_* */
    375:   #endif   /* (__cplusplus) */

    377: /*MC
    378:    PETSC_i - the pure imaginary complex number i

    380:    Level: intermediate

    382: .seealso: `PetscComplex`, `PetscScalar`
    383: M*/
    384: PETSC_EXTERN PetscComplex PETSC_i;

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

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

    404:        So type punning should be portable. */
    405:     union
    406:     {
    407:       PetscComplex z;
    408:       PetscReal    f[2];
    409:     } uz;

    411:     uz.f[0] = x;
    412:     uz.f[1] = y;
    413:     return uz.z;
    414:   }
    415:   #endif
    416: }

    418:   #define MPIU_C_COMPLEX        MPI_C_COMPLEX PETSC_DEPRECATED_MACRO(3, 15, 0, "MPI_C_COMPLEX", )
    419:   #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX PETSC_DEPRECATED_MACRO(3, 15, 0, "MPI_C_DOUBLE_COMPLEX", )

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

    429: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 MPIU___COMPLEX128_ATTR_TAG;

    431:     #undef MPIU___COMPLEX128_ATTR_TAG
    432:   #endif /* PETSC_HAVE_REAL___FLOAT128 */

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

    437:    Level: beginner

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

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

    454: #endif /* PETSC_HAVE_COMPLEX */

    456: /*
    457:     Scalar number definitions
    458:  */
    459: #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
    460:   /*MC
    461:    MPIU_SCALAR - Portable MPI datatype corresponding to `PetscScalar` independent of the precision of `PetscScalar`

    463:    Level: beginner

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

    468: .seealso: `PetscReal`, `PetscScalar`, `PetscComplex`, `PetscInt`, `MPIU_REAL`, `MPIU_COMPLEX`, `MPIU_INT`
    469: M*/
    470:   #define MPIU_SCALAR MPIU_COMPLEX

    472:   /*MC
    473:    PetscRealPart - Returns the real part of a `PetscScalar`

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

    479:    Not Collective

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

    484:    Level: beginner

    486: .seealso: `PetscScalar`, `PetscImaginaryPart()`, `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    487: M*/
    488:   #define PetscRealPart(a) PetscRealPartComplex(a)

    490:   /*MC
    491:    PetscImaginaryPart - Returns the imaginary part of a `PetscScalar`

    493:    Synopsis:
    494: #include <petscmath.h>
    495:    PetscReal PetscImaginaryPart(PetscScalar v)

    497:    Not Collective

    499:    Input Parameter:
    500: .  v - value to find the imaginary part of

    502:    Level: beginner

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

    507: .seealso: `PetscScalar`, `PetscRealPart()`, `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    508: M*/
    509:   #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

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

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

    555: #endif /* PETSC_USE_COMPLEX */

    557: /*
    558:    Certain objects may be created using either single or double precision.
    559:    This is currently not used.
    560: */
    561: typedef enum {
    562:   PETSC_SCALAR_DOUBLE,
    563:   PETSC_SCALAR_SINGLE,
    564:   PETSC_SCALAR_LONG_DOUBLE,
    565:   PETSC_SCALAR_HALF
    566: } PetscScalarPrecision;

    568: /*MC
    569:    PetscAbs - Returns the absolute value of a number

    571:    Synopsis:
    572: #include <petscmath.h>
    573:    type PetscAbs(type v)

    575:    Not Collective

    577:    Input Parameter:
    578: .  v - the number

    580:    Level: beginner

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

    585: .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()`, `PetscSign()`
    586: M*/
    587: #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a)))

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

    592:    Synopsis:
    593: #include <petscmath.h>
    594:    int PetscSign(type v)

    596:    Not Collective

    598:    Input Parameter:
    599: .  v - the number

    601:    Level: beginner

    603:    Note:
    604:    The type can be integer or real floating point value

    606: .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()`
    607: M*/
    608: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)

    610: /*MC
    611:    PetscMin - Returns minimum of two numbers

    613:    Synopsis:
    614: #include <petscmath.h>
    615:    type PetscMin(type v1,type v2)

    617:    Not Collective

    619:    Input Parameters:
    620: +  v1 - first value to find minimum of
    621: -  v2 - second value to find minimum of

    623:    Level: beginner

    625:    Note:
    626:    The type can be integer or floating point value, but cannot be complex

    628: .seealso: `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    629: M*/
    630: #define PetscMin(a, b) (((a) < (b)) ? (a) : (b))

    632: /*MC
    633:    PetscMax - Returns maximum of two numbers

    635:    Synopsis:
    636: #include <petscmath.h>
    637:    type max PetscMax(type v1,type v2)

    639:    Not Collective

    641:    Input Parameters:
    642: +  v1 - first value to find maximum of
    643: -  v2 - second value to find maximum of

    645:    Level: beginner

    647:    Note:
    648:    The type can be integer or floating point value

    650: .seealso: `PetscMin()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    651: M*/
    652: #define PetscMax(a, b) (((a) < (b)) ? (b) : (a))

    654: /*MC
    655:    PetscClipInterval - Returns a number clipped to be within an interval

    657:    Synopsis:
    658: #include <petscmath.h>
    659:    type clip PetscClipInterval(type x,type a,type b)

    661:    Not Collective

    663:    Input Parameters:
    664: +  x - value to use if within interval [a,b]
    665: .  a - lower end of interval
    666: -  b - upper end of interval

    668:    Level: beginner

    670:    Note:
    671:    The type can be integer or floating point value

    673:    Example\:
    674: .vb
    675:   PetscInt c = PetscClipInterval(5, 2, 3); // the value of c is 3
    676:   PetscInt c = PetscClipInterval(5, 2, 6); // the value of c is 5
    677: .ve

    679: .seealso: `PetscMin()`, `PetscMax()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()`
    680: M*/
    681: #define PetscClipInterval(x, a, b) (PetscMax((a), PetscMin((x), (b))))

    683: /*MC
    684:    PetscAbsInt - Returns the absolute value of an integer

    686:    Synopsis:
    687: #include <petscmath.h>
    688:    int abs PetscAbsInt(int v1)

    690:    Input Parameter:
    691: .   v1 - the integer

    693:    Level: beginner

    695: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsReal()`, `PetscSqr()`
    696: M*/
    697: #define PetscAbsInt(a) (((a) < 0) ? (-(a)) : (a))

    699: /*MC
    700:    PetscAbsReal - Returns the absolute value of a real number

    702:    Synopsis:
    703: #include <petscmath.h>
    704:    Real abs PetscAbsReal(PetscReal v1)

    706:    Input Parameter:
    707: .   v1 - the `PetscReal` value

    709:    Level: beginner

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

    723: /*MC
    724:    PetscSqr - Returns the square of a number

    726:    Synopsis:
    727: #include <petscmath.h>
    728:    type sqr PetscSqr(type v1)

    730:    Not Collective

    732:    Input Parameter:
    733: .   v1 - the value

    735:    Level: beginner

    737:    Note:
    738:    The type can be integer, floating point, or complex floating point

    740: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`
    741: M*/
    742: #define PetscSqr(a) ((a) * (a))

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

    748:    Synopsis:
    749: #include <petscmath.h>
    750:    PetscReal PetscRealConstant(real_number)

    752:    Not Collective

    754:    Input Parameter:
    755: .   v1 - the real number, for example 1.5

    757:    Level: beginner

    759:    Note:
    760:    For example, if PETSc is configured with `--with-precision=__float128` and one writes
    761: .vb
    762:    PetscReal d = 1.5;
    763: .ve
    764:    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
    765: .vb
    766:    PetscReal d = PetscRealConstant(1.5);
    767: .ve

    769: .seealso: `PetscReal`
    770: M*/
    771: #if defined(PETSC_USE_REAL_SINGLE)
    772:   #define PetscRealConstant(constant) constant##F
    773: #elif defined(PETSC_USE_REAL_DOUBLE)
    774:   #define PetscRealConstant(constant) constant
    775: #elif defined(PETSC_USE_REAL___FLOAT128)
    776:   #define PetscRealConstant(constant) constant##Q
    777: #elif defined(PETSC_USE_REAL___FP16)
    778:   #define PetscRealConstant(constant) constant##F
    779: #endif

    781: /*
    782:      Basic constants
    783: */
    784: /*MC
    785:   PETSC_PI - the value of $ \pi$ to the correct precision of `PetscReal`.

    787:   Level: beginner

    789: .seealso: `PetscReal`, `PETSC_PHI`, `PETSC_SQRT2`
    790: M*/

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

    795:   Level: beginner

    797: .seealso: `PetscReal`, `PETSC_PI`, `PETSC_SQRT2`
    798: M*/

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

    803:   Level: beginner

    805: .seealso: `PetscReal`, `PETSC_PI`, `PETSC_PHI`
    806: M*/

    808: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
    809: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
    810: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

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

    815:   Level: beginner

    817: .seealso: `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    818: M*/

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

    823:   Level: beginner

    825: .seealso `PETSC_MAX_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    826: M*/

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

    831:   Level: beginner

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

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

    839: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    840: M*/

    842: /*MC
    843:   PETSC_MACHINE_EPSILON - the machine epsilon for the precision of `PetscReal`

    845:   Level: beginner

    847:   Note:
    848:   See <https://en.wikipedia.org/wiki/Machine_epsilon>

    850: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL`
    851: M*/

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

    856:   Level: beginner

    858:   Note:
    859:   See `PETSC_MACHINE_EPSILON`

    861: .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SMALL`
    862: M*/

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

    868:   Level: beginner

    870:   Note:
    871:   See `PETSC_MACHINE_EPSILON`

    873: .seealso `PetscApproximateLTE()`, `PetscApproximateGTE()`, `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`,
    874:          `PETSC_SQRT_MACHINE_EPSILON`
    875: M*/

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

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

    910:   Level: intermediate

    912:   Note:
    913:   This is not the IEEE infinity value

    915: .seealso: `PETSC_NINFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()`
    916: M*/
    917: #define PETSC_INFINITY (PETSC_MAX_REAL / 4)

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

    922:   Level: intermediate

    924:   Note:
    925:   This is not the negative IEEE infinity value

    927: .seealso: `PETSC_INFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()`
    928: M*/
    929: #define PETSC_NINFINITY (-PETSC_INFINITY)

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

    955: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal, PetscReal, PetscReal, PetscReal);
    956: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal, PetscReal);
    957: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar, PetscScalar);

    959: /*@C
    960:   PetscIsCloseAtTolScalar - Like `PetscIsCloseAtTol()` but for `PetscScalar`

    962:   Input Parameters:
    963: + lhs  - The first number
    964: . rhs  - The second number
    965: . rtol - The relative tolerance
    966: - atol - The absolute tolerance

    968:   Level: beginner

    970:   Note:
    971:   This routine is equivalent to `PetscIsCloseAtTol()` when PETSc is configured without complex
    972:   numbers.

    974: .seealso: `PetscIsCloseAtTol()`
    975: @*/
    976: static inline PetscBool PetscIsCloseAtTolScalar(PetscScalar lhs, PetscScalar rhs, PetscReal rtol, PetscReal atol)
    977: {
    978:   PetscBool close = PetscIsCloseAtTol(PetscRealPart(lhs), PetscRealPart(rhs), rtol, atol);

    980:   if (PetscDefined(USE_COMPLEX)) close = (PetscBool)(close && PetscIsCloseAtTol(PetscImaginaryPart(lhs), PetscImaginaryPart(rhs), rtol, atol));
    981:   return close;
    982: }

    984: /*
    985:     These macros are currently hardwired to match the regular data types, so there is no support for a different
    986:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
    987:  */
    988: #define MPIU_MATSCALAR MPIU_SCALAR
    989: typedef PetscScalar MatScalar;
    990: typedef PetscReal   MatReal;

    992: struct petsc_mpiu_2scalar {
    993:   PetscScalar a, b;
    994: };
    995: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2scalar);

    997: /* MPI Datatypes for composite reductions */
    998: struct petsc_mpiu_real_int {
    999:   PetscReal v;
    1000:   PetscInt  i;
    1001: };

    1003: struct petsc_mpiu_scalar_int {
    1004:   PetscScalar v;
    1005:   PetscInt    i;
    1006: };

    1008: PETSC_EXTERN MPI_Datatype MPIU_REAL_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_real_int);
    1009: PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_scalar_int);

    1011: #if defined(PETSC_USE_64BIT_INDICES)
    1012: struct /* __attribute__((packed, aligned(alignof(PetscInt *)))) */ petsc_mpiu_2int {
    1013:   PetscInt a;
    1014:   PetscInt b;
    1015: };
    1016: struct __attribute__((packed)) petsc_mpiu_int_mpiint {
    1017:   PetscInt    a;
    1018:   PetscMPIInt b;
    1019: };
    1020: /*
    1021:  static_assert(sizeof(struct petsc_mpiu_2int) == 2 * sizeof(PetscInt), "");
    1022:  static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt *), "");
    1023:  static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt[2]), "");

    1025:  clang generates warnings that petsc_mpiu_2int is not layout compatible with PetscInt[2] or
    1026:  PetscInt *, even though (with everything else uncommented) both of the static_asserts above
    1027:  pass! So we just comment it out...
    1028: */
    1029: PETSC_EXTERN MPI_Datatype MPIU_2INT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2int) */;
    1030: PETSC_EXTERN MPI_Datatype MPIU_INT_MPIINT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_int_mpiint) */;
    1031: #else
    1032:   #define MPIU_2INT       MPI_2INT
    1033:   #define MPIU_INT_MPIINT MPI_2INT
    1034: #endif
    1035: PETSC_EXTERN MPI_Datatype MPI_4INT;
    1036: PETSC_EXTERN MPI_Datatype MPIU_4INT;

    1038: static inline PetscInt PetscPowInt(PetscInt base, PetscInt power)
    1039: {
    1040:   PetscInt result = 1;
    1041:   while (power) {
    1042:     if (power & 1) result *= base;
    1043:     power >>= 1;
    1044:     if (power) base *= base;
    1045:   }
    1046:   return result;
    1047: }

    1049: static inline PetscInt64 PetscPowInt64(PetscInt base, PetscInt power)
    1050: {
    1051:   PetscInt64 result = 1;
    1052:   while (power) {
    1053:     if (power & 1) result *= base;
    1054:     power >>= 1;
    1055:     if (power) base *= base;
    1056:   }
    1057:   return result;
    1058: }

    1060: static inline PetscReal PetscPowRealInt(PetscReal base, PetscInt power)
    1061: {
    1062:   PetscReal result = 1;
    1063:   if (power < 0) {
    1064:     power = -power;
    1065:     base  = ((PetscReal)1) / base;
    1066:   }
    1067:   while (power) {
    1068:     if (power & 1) result *= base;
    1069:     power >>= 1;
    1070:     if (power) base *= base;
    1071:   }
    1072:   return result;
    1073: }

    1075: static inline PetscScalar PetscPowScalarInt(PetscScalar base, PetscInt power)
    1076: {
    1077:   PetscScalar result = (PetscReal)1;
    1078:   if (power < 0) {
    1079:     power = -power;
    1080:     base  = ((PetscReal)1) / base;
    1081:   }
    1082:   while (power) {
    1083:     if (power & 1) result *= base;
    1084:     power >>= 1;
    1085:     if (power) base *= base;
    1086:   }
    1087:   return result;
    1088: }

    1090: static inline PetscScalar PetscPowScalarReal(PetscScalar base, PetscReal power)
    1091: {
    1092:   PetscScalar cpower = power;
    1093:   return PetscPowScalar(base, cpower);
    1094: }

    1096: /*MC
    1097:    PetscApproximateLTE - Performs a less than or equal to on a given constant with a fudge for floating point numbers

    1099:    Synopsis:
    1100: #include <petscmath.h>
    1101:    bool PetscApproximateLTE(PetscReal x,constant float)

    1103:    Not Collective

    1105:    Input Parameters:
    1106: +   x - the variable
    1107: -   b - the constant float it is checking if `x` is less than or equal to

    1109:    Level: advanced

    1111:    Notes:
    1112:    The fudge factor is the value `PETSC_SMALL`

    1114:    The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    1116:    This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    1117:    floating point results.

    1119:    Example\:
    1120: .vb
    1121:   PetscReal x;
    1122:   if (PetscApproximateLTE(x, 3.2)) { // replaces if (x <= 3.2) {
    1123: .ve

    1125: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateGTE()`
    1126: M*/
    1127: #define PetscApproximateLTE(x, b) ((x) <= (PetscRealConstant(b) + PETSC_SMALL))

    1129: /*MC
    1130:    PetscApproximateGTE - Performs a greater than or equal to on a given constant with a fudge for floating point numbers

    1132:    Synopsis:
    1133: #include <petscmath.h>
    1134:    bool PetscApproximateGTE(PetscReal x,constant float)

    1136:    Not Collective

    1138:    Input Parameters:
    1139: +   x - the variable
    1140: -   b - the constant float it is checking if `x` is greater than or equal to

    1142:    Level: advanced

    1144:    Notes:
    1145:    The fudge factor is the value `PETSC_SMALL`

    1147:    The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2

    1149:    This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
    1150:    floating point results.

    1152:    Example\:
    1153: .vb
    1154:   PetscReal x;
    1155:   if (PetscApproximateGTE(x, 3.2)) {  // replaces if (x >= 3.2) {
    1156: .ve

    1158: .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()`
    1159: M*/
    1160: #define PetscApproximateGTE(x, b) ((x) >= (PetscRealConstant(b) - PETSC_SMALL))

    1162: /*MC
    1163:    PetscCeilInt - Returns the ceiling of the quotation of two positive integers

    1165:    Synopsis:
    1166: #include <petscmath.h>
    1167:    PetscInt PetscCeilInt(PetscInt x,PetscInt y)

    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: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()`
    1183: M*/
    1184: #define PetscCeilInt(x, y) ((((PetscInt)(x)) / ((PetscInt)(y))) + ((((PetscInt)(x)) % ((PetscInt)(y))) ? 1 : 0))

    1186: #define PetscCeilInt64(x, y) ((((PetscInt64)(x)) / ((PetscInt64)(y))) + ((((PetscInt64)(x)) % ((PetscInt64)(y))) ? 1 : 0))

    1188: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt, const PetscReal[], const PetscReal[], PetscReal *, PetscReal *);