xref: /petsc/include/petscmath.h (revision 092991ac1244d667ecf45705734b89bd49b3016b)

/*

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

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

*/

#if !defined(PETSCMATH_H)
#define PETSCMATH_H
#include <math.h>
#include <petscsystypes.h>

/*

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

*/

/*
    Real number definitions
 */
#if defined(PETSC_USE_REAL_SINGLE)
#define PetscSqrtReal(a)    sqrtf(a)
#define PetscCbrtReal(a)    cbrtf(a)
#define PetscHypotReal(a,b) hypotf(a,b)
#define PetscAtan2Real(a,b) atan2f(a,b)
#define PetscPowReal(a,b)   powf(a,b)
#define PetscExpReal(a)     expf(a)
#define PetscLogReal(a)     logf(a)
#define PetscLog10Real(a)   log10f(a)
#define PetscLog2Real(a)    log2f(a)
#define PetscSinReal(a)     sinf(a)
#define PetscCosReal(a)     cosf(a)
#define PetscTanReal(a)     tanf(a)
#define PetscAsinReal(a)    asinf(a)
#define PetscAcosReal(a)    acosf(a)
#define PetscAtanReal(a)    atanf(a)
#define PetscSinhReal(a)    sinhf(a)
#define PetscCoshReal(a)    coshf(a)
#define PetscTanhReal(a)    tanhf(a)
#define PetscAsinhReal(a)   asinhf(a)
#define PetscAcoshReal(a)   acoshf(a)
#define PetscAtanhReal(a)   atanhf(a)
#define PetscCeilReal(a)    ceilf(a)
#define PetscFloorReal(a)   floorf(a)
#define PetscFmodReal(a,b)  fmodf(a,b)
#define PetscTGamma(a)      tgammaf(a)
#if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
#define PetscLGamma(a)      gammaf(a)
#else
#define PetscLGamma(a)      lgammaf(a)
#endif

#elif defined(PETSC_USE_REAL_DOUBLE)
#define PetscSqrtReal(a)    sqrt(a)
#define PetscCbrtReal(a)    cbrt(a)
#define PetscHypotReal(a,b) hypot(a,b)
#define PetscAtan2Real(a,b) atan2(a,b)
#define PetscPowReal(a,b)   pow(a,b)
#define PetscExpReal(a)     exp(a)
#define PetscLogReal(a)     log(a)
#define PetscLog10Real(a)   log10(a)
#define PetscLog2Real(a)    log2(a)
#define PetscSinReal(a)     sin(a)
#define PetscCosReal(a)     cos(a)
#define PetscTanReal(a)     tan(a)
#define PetscAsinReal(a)    asin(a)
#define PetscAcosReal(a)    acos(a)
#define PetscAtanReal(a)    atan(a)
#define PetscSinhReal(a)    sinh(a)
#define PetscCoshReal(a)    cosh(a)
#define PetscTanhReal(a)    tanh(a)
#define PetscAsinhReal(a)   asinh(a)
#define PetscAcoshReal(a)   acosh(a)
#define PetscAtanhReal(a)   atanh(a)
#define PetscCeilReal(a)    ceil(a)
#define PetscFloorReal(a)   floor(a)
#define PetscFmodReal(a,b)  fmod(a,b)
#define PetscTGamma(a)      tgamma(a)
#if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
#define PetscLGamma(a)      gamma(a)
#else
#define PetscLGamma(a)      lgamma(a)
#endif

#elif defined(PETSC_USE_REAL___FLOAT128)
#define PetscSqrtReal(a)    sqrtq(a)
#define PetscCbrtReal(a)    cbrtq(a)
#define PetscHypotReal(a,b) hypotq(a,b)
#define PetscAtan2Real(a,b) atan2q(a,b)
#define PetscPowReal(a,b)   powq(a,b)
#define PetscExpReal(a)     expq(a)
#define PetscLogReal(a)     logq(a)
#define PetscLog10Real(a)   log10q(a)
#define PetscLog2Real(a)    log2q(a)
#define PetscSinReal(a)     sinq(a)
#define PetscCosReal(a)     cosq(a)
#define PetscTanReal(a)     tanq(a)
#define PetscAsinReal(a)    asinq(a)
#define PetscAcosReal(a)    acosq(a)
#define PetscAtanReal(a)    atanq(a)
#define PetscSinhReal(a)    sinhq(a)
#define PetscCoshReal(a)    coshq(a)
#define PetscTanhReal(a)    tanhq(a)
#define PetscAsinhReal(a)   asinhq(a)
#define PetscAcoshReal(a)   acoshq(a)
#define PetscAtanhReal(a)   atanhq(a)
#define PetscCeilReal(a)    ceilq(a)
#define PetscFloorReal(a)   floorq(a)
#define PetscFmodReal(a,b)  fmodq(a,b)
#define PetscTGamma(a)      tgammaq(a)
#if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
#define PetscLGamma(a)      gammaq(a)
#else
#define PetscLGamma(a)      lgammaq(a)
#endif

#elif defined(PETSC_USE_REAL___FP16)
#define PetscSqrtReal(a)    sqrtf(a)
#define PetscCbrtReal(a)    cbrtf(a)
#define PetscHypotReal(a,b) hypotf(a,b)
#define PetscAtan2Real(a,b) atan2f(a,b)
#define PetscPowReal(a,b)   powf(a,b)
#define PetscExpReal(a)     expf(a)
#define PetscLogReal(a)     logf(a)
#define PetscLog10Real(a)   log10f(a)
#define PetscLog2Real(a)    log2f(a)
#define PetscSinReal(a)     sinf(a)
#define PetscCosReal(a)     cosf(a)
#define PetscTanReal(a)     tanf(a)
#define PetscAsinReal(a)    asinf(a)
#define PetscAcosReal(a)    acosf(a)
#define PetscAtanReal(a)    atanf(a)
#define PetscSinhReal(a)    sinhf(a)
#define PetscCoshReal(a)    coshf(a)
#define PetscTanhReal(a)    tanhf(a)
#define PetscAsinhReal(a)   asinhf(a)
#define PetscAcoshReal(a)   acoshf(a)
#define PetscAtanhReal(a)   atanhf(a)
#define PetscCeilReal(a)    ceilf(a)
#define PetscFloorReal(a)   floorf(a)
#define PetscFmodReal(a,b)  fmodf(a,b)
#define PetscTGamma(a)      tgammaf(a)
#if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
#define PetscLGamma(a)      gammaf(a)
#else
#define PetscLGamma(a)      lgammaf(a)
#endif

#endif /* PETSC_USE_REAL_* */

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

#if !defined(PETSC_HAVE_LOG2)
#undef PetscLog2Real
PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
{
  return PetscLogReal(a)/PetscLogReal((PetscReal)2);
}
#endif

#if defined(PETSC_USE_REAL___FLOAT128)
PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
#endif
#if defined(PETSC_USE_REAL___FP16)
PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
#endif

/*MC
   MPIU_REAL - MPI datatype corresponding to PetscReal

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

   Level: beginner

.seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
M*/
#if defined(PETSC_USE_REAL_SINGLE)
#  define MPIU_REAL MPI_FLOAT
#elif defined(PETSC_USE_REAL_DOUBLE)
#  define MPIU_REAL MPI_DOUBLE
#elif defined(PETSC_USE_REAL___FLOAT128)
#  define MPIU_REAL MPIU___FLOAT128
#elif defined(PETSC_USE_REAL___FP16)
#  define MPIU_REAL MPIU___FP16
#endif /* PETSC_USE_REAL_* */

/*
    Complex number definitions
 */
#if defined(PETSC_HAVE_COMPLEX)
#if defined(__cplusplus)
/* C++ support of complex number */

#define PetscRealPartComplex(a)      (a).real()
#define PetscImaginaryPartComplex(a) (a).imag()
#define PetscAbsComplex(a)           petsccomplexlib::abs(a)
#define PetscArgComplex(a)           petsccomplexlib::arg(a)
#define PetscConjComplex(a)          petsccomplexlib::conj(a)
#define PetscSqrtComplex(a)          petsccomplexlib::sqrt(a)
#define PetscPowComplex(a,b)         petsccomplexlib::pow(a,b)
#define PetscExpComplex(a)           petsccomplexlib::exp(a)
#define PetscLogComplex(a)           petsccomplexlib::log(a)
#define PetscSinComplex(a)           petsccomplexlib::sin(a)
#define PetscCosComplex(a)           petsccomplexlib::cos(a)
#define PetscTanComplex(a)           petsccomplexlib::tan(a)
#define PetscAsinComplex(a)          petsccomplexlib::asin(a)
#define PetscAcosComplex(a)          petsccomplexlib::acos(a)
#define PetscAtanComplex(a)          petsccomplexlib::atan(a)
#define PetscSinhComplex(a)          petsccomplexlib::sinh(a)
#define PetscCoshComplex(a)          petsccomplexlib::cosh(a)
#define PetscTanhComplex(a)          petsccomplexlib::tanh(a)
#define PetscAsinhComplex(a)         petsccomplexlib::asinh(a)
#define PetscAcoshComplex(a)         petsccomplexlib::acosh(a)
#define PetscAtanhComplex(a)         petsccomplexlib::atanh(a)

/* TODO: Add configure tests

#if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
#undef PetscTanComplex
PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
{
  return PetscSinComplex(z)/PetscCosComplex(z);
}
#endif

#if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
#undef PetscTanhComplex
PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
{
  return PetscSinhComplex(z)/PetscCoshComplex(z);
}
#endif

#if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
#undef PetscAsinComplex
PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
{
  const PetscComplex j(0,1);
  return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
}
#endif

#if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
#undef PetscAcosComplex
PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
{
  const PetscComplex j(0,1);
  return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
}
#endif

#if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
#undef PetscAtanComplex
PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
{
  const PetscComplex j(0,1);
  return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
}
#endif

#if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
#undef PetscAsinhComplex
PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
{
  return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
}
#endif

#if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
#undef PetscAcoshComplex
PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
{
  return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
}
#endif

#if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
#undef PetscAtanhComplex
PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
{
  return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
}
#endif

*/

#else /* C99 support of complex number */

#if defined(PETSC_USE_REAL_SINGLE)
#define PetscRealPartComplex(a)      crealf(a)
#define PetscImaginaryPartComplex(a) cimagf(a)
#define PetscAbsComplex(a)           cabsf(a)
#define PetscArgComplex(a)           cargf(a)
#define PetscConjComplex(a)          conjf(a)
#define PetscSqrtComplex(a)          csqrtf(a)
#define PetscPowComplex(a,b)         cpowf(a,b)
#define PetscExpComplex(a)           cexpf(a)
#define PetscLogComplex(a)           clogf(a)
#define PetscSinComplex(a)           csinf(a)
#define PetscCosComplex(a)           ccosf(a)
#define PetscTanComplex(a)           ctanf(a)
#define PetscAsinComplex(a)          casinf(a)
#define PetscAcosComplex(a)          cacosf(a)
#define PetscAtanComplex(a)          catanf(a)
#define PetscSinhComplex(a)          csinhf(a)
#define PetscCoshComplex(a)          ccoshf(a)
#define PetscTanhComplex(a)          ctanhf(a)
#define PetscAsinhComplex(a)         casinhf(a)
#define PetscAcoshComplex(a)         cacoshf(a)
#define PetscAtanhComplex(a)         catanhf(a)

#elif defined(PETSC_USE_REAL_DOUBLE)
#define PetscRealPartComplex(a)      creal(a)
#define PetscImaginaryPartComplex(a) cimag(a)
#define PetscAbsComplex(a)           cabs(a)
#define PetscArgComplex(a)           carg(a)
#define PetscConjComplex(a)          conj(a)
#define PetscSqrtComplex(a)          csqrt(a)
#define PetscPowComplex(a,b)         cpow(a,b)
#define PetscExpComplex(a)           cexp(a)
#define PetscLogComplex(a)           clog(a)
#define PetscSinComplex(a)           csin(a)
#define PetscCosComplex(a)           ccos(a)
#define PetscTanComplex(a)           ctan(a)
#define PetscAsinComplex(a)          casin(a)
#define PetscAcosComplex(a)          cacos(a)
#define PetscAtanComplex(a)          catan(a)
#define PetscSinhComplex(a)          csinh(a)
#define PetscCoshComplex(a)          ccosh(a)
#define PetscTanhComplex(a)          ctanh(a)
#define PetscAsinhComplex(a)         casinh(a)
#define PetscAcoshComplex(a)         cacosh(a)
#define PetscAtanhComplex(a)         catanh(a)

#elif defined(PETSC_USE_REAL___FLOAT128)
#define PetscRealPartComplex(a)      crealq(a)
#define PetscImaginaryPartComplex(a) cimagq(a)
#define PetscAbsComplex(a)           cabsq(a)
#define PetscArgComplex(a)           cargq(a)
#define PetscConjComplex(a)          conjq(a)
#define PetscSqrtComplex(a)          csqrtq(a)
#define PetscPowComplex(a,b)         cpowq(a,b)
#define PetscExpComplex(a)           cexpq(a)
#define PetscLogComplex(a)           clogq(a)
#define PetscSinComplex(a)           csinq(a)
#define PetscCosComplex(a)           ccosq(a)
#define PetscTanComplex(a)           ctanq(a)
#define PetscAsinComplex(a)          casinq(a)
#define PetscAcosComplex(a)          cacosq(a)
#define PetscAtanComplex(a)          catanq(a)
#define PetscSinhComplex(a)          csinhq(a)
#define PetscCoshComplex(a)          ccoshq(a)
#define PetscTanhComplex(a)          ctanhq(a)
#define PetscAsinhComplex(a)         casinhq(a)
#define PetscAcoshComplex(a)         cacoshq(a)
#define PetscAtanhComplex(a)         catanhq(a)

#endif /* PETSC_USE_REAL_* */
#endif /* (__cplusplus) */

/*
   PETSC_i is the imaginary number, i
*/
PETSC_EXTERN PetscComplex PETSC_i;

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

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

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

    uz.f[0] = x;
    uz.f[1] = y;
    return uz.z;
  }
#endif
}

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

#if defined(PETSC_USE_REAL___FLOAT128)
PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
#endif /* PETSC_USE_REAL___FLOAT128 */

/*MC
   MPIU_COMPLEX - MPI datatype corresponding to PetscComplex

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

   Level: beginner

.seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
M*/
#if defined(PETSC_USE_REAL_SINGLE)
#  define MPIU_COMPLEX MPI_C_COMPLEX
#elif defined(PETSC_USE_REAL_DOUBLE)
#  define MPIU_COMPLEX MPI_C_DOUBLE_COMPLEX
#elif defined(PETSC_USE_REAL___FLOAT128)
#  define MPIU_COMPLEX MPIU___COMPLEX128
#elif defined(PETSC_USE_REAL___FP16)
#  define MPIU_COMPLEX MPI_C_COMPLEX
#endif /* PETSC_USE_REAL_* */

#endif /* PETSC_HAVE_COMPLEX */

/*
    Scalar number definitions
 */
#if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
/*MC
   MPIU_SCALAR - MPI datatype corresponding to PetscScalar

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

   Level: beginner

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

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

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

   Not Collective

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

   Level: beginner

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

M*/
#define PetscRealPart(a)      PetscRealPartComplex(a)

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

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

   Not Collective

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

   Level: beginner

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

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

M*/
#define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

#define PetscAbsScalar(a)     PetscAbsComplex(a)
#define PetscArgScalar(a)     PetscArgComplex(a)
#define PetscConj(a)          PetscConjComplex(a)
#define PetscSqrtScalar(a)    PetscSqrtComplex(a)
#define PetscPowScalar(a,b)   PetscPowComplex(a,b)
#define PetscExpScalar(a)     PetscExpComplex(a)
#define PetscLogScalar(a)     PetscLogComplex(a)
#define PetscSinScalar(a)     PetscSinComplex(a)
#define PetscCosScalar(a)     PetscCosComplex(a)
#define PetscTanScalar(a)     PetscTanComplex(a)
#define PetscAsinScalar(a)    PetscAsinComplex(a)
#define PetscAcosScalar(a)    PetscAcosComplex(a)
#define PetscAtanScalar(a)    PetscAtanComplex(a)
#define PetscSinhScalar(a)    PetscSinhComplex(a)
#define PetscCoshScalar(a)    PetscCoshComplex(a)
#define PetscTanhScalar(a)    PetscTanhComplex(a)
#define PetscAsinhScalar(a)   PetscAsinhComplex(a)
#define PetscAcoshScalar(a)   PetscAcoshComplex(a)
#define PetscAtanhScalar(a)   PetscAtanhComplex(a)

#else /* PETSC_USE_COMPLEX */
#define MPIU_SCALAR MPIU_REAL
#define PetscRealPart(a)      (a)
#define PetscImaginaryPart(a) ((PetscReal)0)
#define PetscAbsScalar(a)     PetscAbsReal(a)
#define PetscArgScalar(a)     (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
#define PetscConj(a)          (a)
#define PetscSqrtScalar(a)    PetscSqrtReal(a)
#define PetscPowScalar(a,b)   PetscPowReal(a,b)
#define PetscExpScalar(a)     PetscExpReal(a)
#define PetscLogScalar(a)     PetscLogReal(a)
#define PetscSinScalar(a)     PetscSinReal(a)
#define PetscCosScalar(a)     PetscCosReal(a)
#define PetscTanScalar(a)     PetscTanReal(a)
#define PetscAsinScalar(a)    PetscAsinReal(a)
#define PetscAcosScalar(a)    PetscAcosReal(a)
#define PetscAtanScalar(a)    PetscAtanReal(a)
#define PetscSinhScalar(a)    PetscSinhReal(a)
#define PetscCoshScalar(a)    PetscCoshReal(a)
#define PetscTanhScalar(a)    PetscTanhReal(a)
#define PetscAsinhScalar(a)   PetscAsinhReal(a)
#define PetscAcoshScalar(a)   PetscAcoshReal(a)
#define PetscAtanhScalar(a)   PetscAtanhReal(a)

#endif /* PETSC_USE_COMPLEX */

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

/* --------------------------------------------------------------------------*/

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

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

   Not Collective

   Input Parameter:
.  v - the number

   Notes:
    type can be integer or real floating point value

   Level: beginner

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

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

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

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

   Not Collective

   Input Parameter:
.  v - the number

   Notes:
    type can be integer or real floating point value

   Level: beginner

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

/*MC
   PetscMin - Returns minimum of two numbers

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

   Not Collective

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

   Notes:
    type can be integer or floating point value

   Level: beginner

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

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

/*MC
   PetscMax - Returns maxium of two numbers

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

   Not Collective

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

   Notes:
    type can be integer or floating point value

   Level: beginner

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

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

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

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

   Not Collective

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

   Notes:
    type can be integer or floating point value

   Level: beginner

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

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

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

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

   Not Collective

   Input Parameter:
.   v1 - the integer

   Level: beginner

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

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

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

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

   Not Collective

   Input Parameter:
.   v1 - the double

   Level: beginner

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

M*/
#if defined(PETSC_USE_REAL_SINGLE)
#define PetscAbsReal(a) fabsf(a)
#elif defined(PETSC_USE_REAL_DOUBLE)
#define PetscAbsReal(a) fabs(a)
#elif defined(PETSC_USE_REAL___FLOAT128)
#define PetscAbsReal(a) fabsq(a)
#elif defined(PETSC_USE_REAL___FP16)
#define PetscAbsReal(a) fabsf(a)
#endif

/*MC
   PetscSqr - Returns the square of a number

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

   Not Collective

   Input Parameter:
.   v1 - the value

   Notes:
    type can be integer or floating point value

   Level: beginner

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

M*/
#define PetscSqr(a)     ((a)*(a))

/* ----------------------------------------------------------------------------*/

#if defined(PETSC_USE_REAL_SINGLE)
#define PetscRealConstant(constant) constant##F
#elif defined(PETSC_USE_REAL_DOUBLE)
#define PetscRealConstant(constant) constant
#elif defined(PETSC_USE_REAL___FLOAT128)
#define PetscRealConstant(constant) constant##Q
#elif defined(PETSC_USE_REAL___FP16)
#define PetscRealConstant(constant) constant##F
#endif

/*
     Basic constants
*/
#define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
#define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
#define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

#if !defined(PETSC_USE_64BIT_INDICES)
#define PETSC_MAX_INT            2147483647
#define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
#else
#define PETSC_MAX_INT            9223372036854775807L
#define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
#endif
#define PETSC_MAX_UINT16         65535

#if defined(PETSC_USE_REAL_SINGLE)
#  define PETSC_MAX_REAL                3.40282346638528860e+38F
#  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
#  define PETSC_MACHINE_EPSILON         1.19209290e-07F
#  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
#  define PETSC_SMALL                   1.e-5F
#elif defined(PETSC_USE_REAL_DOUBLE)
#  define PETSC_MAX_REAL                1.7976931348623157e+308
#  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
#  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
#  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
#  define PETSC_SMALL                   1.e-10
#elif defined(PETSC_USE_REAL___FLOAT128)
#  define PETSC_MAX_REAL                FLT128_MAX
#  define PETSC_MIN_REAL                (-FLT128_MAX)
#  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
#  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078144567552953958511352539e-17Q
#  define PETSC_SMALL                   1.e-20Q
#elif defined(PETSC_USE_REAL___FP16)
#  define PETSC_MAX_REAL                65504.0F
#  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
#  define PETSC_MACHINE_EPSILON         .0009765625F
#  define PETSC_SQRT_MACHINE_EPSILON    .03125F
#  define PETSC_SMALL                   5.e-3F
#endif

#define PETSC_INFINITY               (PETSC_MAX_REAL/4)
#define PETSC_NINFINITY              (-PETSC_INFINITY)

PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}

PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);

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

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

/*
   MPI Datatypes for composite reductions:
   MPIU_REAL_INT -> struct { PetscReal; PetscInt; }
   MPIU_SCALAR_INT -> struct { PetscScalar; PetscInt; }
*/
PETSC_EXTERN MPI_Datatype MPIU_REAL_INT;
PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT;

#if defined(PETSC_USE_64BIT_INDICES)
struct petsc_mpiu_2int {PetscInt a,b;};
PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
#else
#define MPIU_2INT MPI_2INT
#endif

PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
{
  PetscInt result = 1;
  while (power) {
    if (power & 1) result *= base;
    power >>= 1;
    base *= base;
  }
  return result;
}

PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
{
  PetscInt64 result = 1;
  while (power) {
    if (power & 1) result *= base;
    power >>= 1;
    base *= base;
  }
  return result;
}

PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
{
  PetscReal result = 1;
  if (power < 0) {
    power = -power;
    base  = ((PetscReal)1)/base;
  }
  while (power) {
    if (power & 1) result *= base;
    power >>= 1;
    base *= base;
  }
  return result;
}

PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
{
  PetscScalar result = (PetscReal)1;
  if (power < 0) {
    power = -power;
    base  = ((PetscReal)1)/base;
  }
  while (power) {
    if (power & 1) result *= base;
    power >>= 1;
    base *= base;
  }
  return result;
}

PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
{
  PetscScalar cpower = power;
  return PetscPowScalar(base,cpower);
}

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

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

   Not Collective

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

   Notes:
     The fudge factor is the value PETSC_SMALL

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

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

   Level: advanced

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

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

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

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

   Not Collective

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

   Notes:
     The fudge factor is the value PETSC_SMALL

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

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

   Level: advanced

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

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

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