/* 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. */ #pragma once #include #include #include /* SUBMANSEC = Sys */ /* 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 PetscErfReal(a) erff(a) #define PetscCeilReal(a) ceilf(a) #define PetscFloorReal(a) floorf(a) #define PetscRintReal(a) rintf(a) #define PetscFmodReal(a, b) fmodf(a, b) #define PetscCopysignReal(a, b) copysignf(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 PetscErfReal(a) erf(a) #define PetscCeilReal(a) ceil(a) #define PetscFloorReal(a) floor(a) #define PetscRintReal(a) rint(a) #define PetscFmodReal(a, b) fmod(a, b) #define PetscCopysignReal(a, b) copysign(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 PetscErfReal(a) erfq(a) #define PetscCeilReal(a) ceilq(a) #define PetscFloorReal(a) floorq(a) #define PetscRintReal(a) rintq(a) #define PetscFmodReal(a, b) fmodq(a, b) #define PetscCopysignReal(a, b) copysignq(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 PetscErfReal(a) erff(a) #define PetscCeilReal(a) ceilf(a) #define PetscFloorReal(a) floorf(a) #define PetscRintReal(a) rintf(a) #define PetscFmodReal(a, b) fmodf(a, b) #define PetscCopysignReal(a, b) copysignf(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_* */ static inline PetscReal PetscSignReal(PetscReal a) { return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0)); } #if !defined(PETSC_HAVE_LOG2) #undef PetscLog2Real static inline PetscReal PetscLog2Real(PetscReal a) { return PetscLogReal(a) / PetscLogReal((PetscReal)2); } #endif #if defined(PETSC_HAVE_REAL___FLOAT128) && !defined(PETSC_SKIP_REAL___FLOAT128) PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__float128); #endif #if defined(PETSC_HAVE_REAL___FP16) && !defined(PETSC_SKIP_REAL___FP16) PETSC_EXTERN MPI_Datatype MPIU___FP16 PETSC_ATTRIBUTE_MPI_TYPE_TAG(__fp16); #endif /*MC MPIU_REAL - Portable MPI datatype corresponding to `PetscReal` independent of what precision `PetscReal` is in Level: beginner Note: In MPI calls that require an MPI datatype that matches a `PetscReal` or array of `PetscReal` values, pass this value. .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) && !defined(PETSC_USE_REAL___FLOAT128) /* C++ support of complex number */ #define PetscRealPartComplex(a) (static_cast(a)).real() #define PetscImaginaryPartComplex(a) (static_cast(a)).imag() #define PetscAbsComplex(a) petsccomplexlib::abs(static_cast(a)) #define PetscArgComplex(a) petsccomplexlib::arg(static_cast(a)) #define PetscConjComplex(a) petsccomplexlib::conj(static_cast(a)) #define PetscSqrtComplex(a) petsccomplexlib::sqrt(static_cast(a)) #define PetscPowComplex(a, b) petsccomplexlib::pow(static_cast(a), static_cast(b)) #define PetscExpComplex(a) petsccomplexlib::exp(static_cast(a)) #define PetscLogComplex(a) petsccomplexlib::log(static_cast(a)) #define PetscSinComplex(a) petsccomplexlib::sin(static_cast(a)) #define PetscCosComplex(a) petsccomplexlib::cos(static_cast(a)) #define PetscTanComplex(a) petsccomplexlib::tan(static_cast(a)) #define PetscAsinComplex(a) petsccomplexlib::asin(static_cast(a)) #define PetscAcosComplex(a) petsccomplexlib::acos(static_cast(a)) #define PetscAtanComplex(a) petsccomplexlib::atan(static_cast(a)) #define PetscSinhComplex(a) petsccomplexlib::sinh(static_cast(a)) #define PetscCoshComplex(a) petsccomplexlib::cosh(static_cast(a)) #define PetscTanhComplex(a) petsccomplexlib::tanh(static_cast(a)) #define PetscAsinhComplex(a) petsccomplexlib::asinh(static_cast(a)) #define PetscAcoshComplex(a) petsccomplexlib::acosh(static_cast(a)) #define PetscAtanhComplex(a) petsccomplexlib::atanh(static_cast(a)) /* TODO: Add configure tests #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX) #undef PetscTanComplex static inline PetscComplex PetscTanComplex(PetscComplex z) { return PetscSinComplex(z)/PetscCosComplex(z); } #endif #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX) #undef PetscTanhComplex static inline PetscComplex PetscTanhComplex(PetscComplex z) { return PetscSinhComplex(z)/PetscCoshComplex(z); } #endif #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX) #undef PetscAsinComplex 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 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 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 static inline PetscComplex PetscAsinhComplex(PetscComplex z) { return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f)); } #endif #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX) #undef PetscAcoshComplex static inline PetscComplex PetscAcoshComplex(PetscComplex z) { return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f)); } #endif #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX) #undef PetscAtanhComplex 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) */ /*MC PETSC_i - the pure imaginary complex number i Level: intermediate .seealso: `PetscComplex`, `PetscScalar` M*/ 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 */ static inline PetscComplex PetscCMPLX(PetscReal x, PetscReal y) { #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128) 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(3, 15, 0, "MPI_C_COMPLEX", ) #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX PETSC_DEPRECATED_MACRO(3, 15, 0, "MPI_C_DOUBLE_COMPLEX", ) #if defined(PETSC_HAVE_REAL___FLOAT128) && !defined(PETSC_SKIP_REAL___FLOAT128) // if complex is not used, then quadmath.h won't be included by petscsystypes.h #if defined(PETSC_USE_COMPLEX) #define MPIU___COMPLEX128_ATTR_TAG PETSC_ATTRIBUTE_MPI_TYPE_TAG(__complex128) #else #define MPIU___COMPLEX128_ATTR_TAG #endif PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 MPIU___COMPLEX128_ATTR_TAG; #undef MPIU___COMPLEX128_ATTR_TAG #endif /* PETSC_HAVE_REAL___FLOAT128 */ /*MC MPIU_COMPLEX - Portable MPI datatype corresponding to `PetscComplex` independent of the precision of `PetscComplex` Level: beginner Note: In MPI calls that require an MPI datatype that matches a `PetscComplex` or array of `PetscComplex` values, pass this value. .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 - Portable MPI datatype corresponding to `PetscScalar` independent of the precision of `PetscScalar` Level: beginner Note: In MPI calls that require an MPI datatype that matches a `PetscScalar` or array of `PetscScalar` values, pass this value. .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 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 PetscReal PetscImaginaryPart(PetscScalar v) Not Collective Input Parameter: . v - value to find the imaginary part of Level: beginner Note: 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 type PetscAbs(type v) Not Collective Input Parameter: . v - the number Level: beginner Note: The type can be integer or real floating point value, but cannot be complex .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()`, `PetscSign()` M*/ #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a))) /*MC PetscSign - Returns the sign of a number as an integer of value -1, 0, or 1 Synopsis: #include int PetscSign(type v) Not Collective Input Parameter: . v - the number Level: beginner Note: The type can be integer or real floating point value .seealso: `PetscAbsInt()`, `PetscAbsReal()`, `PetscAbsScalar()` M*/ #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1) /*MC PetscMin - Returns minimum of two numbers Synopsis: #include type PetscMin(type v1,type v2) Not Collective Input Parameters: + v1 - first value to find minimum of - v2 - second value to find minimum of Level: beginner Note: The type can be integer or floating point value, but cannot be complex .seealso: `PetscMax()`, `PetscClipInterval()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscSqr()` M*/ #define PetscMin(a, b) (((a) < (b)) ? (a) : (b)) /*MC PetscMax - Returns maximum of two numbers Synopsis: #include type max PetscMax(type v1,type v2) Not Collective Input Parameters: + v1 - first value to find maximum of - v2 - second value to find maximum of Level: beginner Note: The type can be integer or floating point value .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 type clip PetscClipInterval(type x,type a,type b) Not Collective Input Parameters: + x - value to use if within interval [a,b] . a - lower end of interval - b - upper end of interval Level: beginner Note: The type can be integer or floating point value Example\: .vb PetscInt c = PetscClipInterval(5, 2, 3); // the value of c is 3 PetscInt c = PetscClipInterval(5, 2, 6); // the value of c is 5 .ve .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 int abs PetscAbsInt(int v1) 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 a real number Synopsis: #include Real abs PetscAbsReal(PetscReal v1) Input Parameter: . v1 - the `PetscReal` value Level: beginner .seealso: `PetscReal`, `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 type sqr PetscSqr(type v1) Not Collective Input Parameter: . v1 - the value Level: beginner Note: The type can be integer, floating point, or complex floating point .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()` M*/ #define PetscSqr(a) ((a) * (a)) /*MC PetscRealConstant - a compile time macro that ensures a given constant real number is properly represented in the configured precision of `PetscReal` be it half, single, double or 128-bit representation Synopsis: #include PetscReal PetscRealConstant(real_number) Not Collective Input Parameter: . v1 - the real number, for example 1.5 Level: beginner Note: For example, if PETSc is configured with `--with-precision=__float128` and one writes .vb PetscReal d = 1.5; .ve 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 .vb PetscReal d = PetscRealConstant(1.5); .ve .seealso: `PetscReal` M*/ #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 */ /*MC PETSC_PI - the value of $ \pi$ to the correct precision of `PetscReal`. Level: beginner .seealso: `PetscReal`, `PETSC_PHI`, `PETSC_SQRT2` M*/ /*MC PETSC_PHI - the value of $ \phi$, the Golden Ratio, to the correct precision of `PetscReal`. Level: beginner .seealso: `PetscReal`, `PETSC_PI`, `PETSC_SQRT2` M*/ /*MC PETSC_SQRT2 - the value of $ \sqrt{2} $ to the correct precision of `PetscReal`. Level: beginner .seealso: `PetscReal`, `PETSC_PI`, `PETSC_PHI` M*/ #define PETSC_PI PetscRealConstant(3.1415926535897932384626433832795029) #define PETSC_PHI PetscRealConstant(1.6180339887498948482045868343656381) #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981) /*MC PETSC_MAX_REAL - the largest real value that can be stored in a `PetscReal` Level: beginner .seealso: `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL` M*/ /*MC PETSC_MIN_REAL - the smallest real value that can be stored in a `PetscReal`, generally this is - `PETSC_MAX_REAL` Level: beginner .seealso `PETSC_MAX_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL` M*/ /*MC PETSC_REAL_MIN - the smallest positive normalized real value that can be stored in a `PetscReal`. Level: beginner Note: See for a discussion of normalized and subnormal floating point numbers Developer Note: The naming is confusing as there is both a `PETSC_REAL_MIN` and `PETSC_MIN_REAL` with different meanings. .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL` M*/ /*MC PETSC_MACHINE_EPSILON - the machine epsilon for the precision of `PetscReal` Level: beginner Note: See .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_SQRT_MACHINE_EPSILON`, `PETSC_SMALL` M*/ /*MC PETSC_SQRT_MACHINE_EPSILON - the square root of the machine epsilon for the precision of `PetscReal` Level: beginner Note: See `PETSC_MACHINE_EPSILON` .seealso `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SMALL` M*/ /*MC PETSC_SMALL - an arbitrary "small" number which depends on the precision of `PetscReal` used in some PETSc examples and in `PetscApproximateLTE()` and `PetscApproximateGTE()` to determine if a computation was successful. Level: beginner Note: See `PETSC_MACHINE_EPSILON` .seealso `PetscApproximateLTE()`, `PetscApproximateGTE()`, `PETSC_MAX_REAL`, `PETSC_MIN_REAL`, `PETSC_REAL_MIN`, `PETSC_MACHINE_EPSILON`, `PETSC_SQRT_MACHINE_EPSILON` M*/ #if defined(PETSC_USE_REAL_SINGLE) #define PETSC_MAX_REAL 3.40282346638528860e+38F #define PETSC_MIN_REAL (-PETSC_MAX_REAL) #define PETSC_REAL_MIN 1.1754944e-38F #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_REAL_MIN 2.225073858507201e-308 #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_REAL_MIN FLT128_MIN #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_REAL_MIN .00006103515625F #define PETSC_MACHINE_EPSILON .0009765625F #define PETSC_SQRT_MACHINE_EPSILON .03125F #define PETSC_SMALL 5.e-3F #endif /*MC PETSC_INFINITY - a finite number that represents infinity for setting certain bounds in `Tao` Level: intermediate Note: This is not the IEEE infinity value .seealso: `PETSC_NINFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()` M*/ #define PETSC_INFINITY (PETSC_MAX_REAL / 4) /*MC PETSC_NINFINITY - a finite number that represents negative infinity for setting certain bounds in `Tao` Level: intermediate Note: This is not the negative IEEE infinity value .seealso: `PETSC_INFINITY`, `SNESVIGetVariableBounds()`, `SNESVISetComputeVariableBounds()`, `SNESVISetVariableBounds()` M*/ #define PETSC_NINFINITY (-PETSC_INFINITY) PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal); PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal); PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal); static inline PetscBool PetscIsInfOrNanReal(PetscReal v) { return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE; } static inline PetscBool PetscIsInfScalar(PetscScalar v) { return PetscIsInfReal(PetscAbsScalar(v)); } static inline PetscBool PetscIsNanScalar(PetscScalar v) { return PetscIsNanReal(PetscAbsScalar(v)); } static inline PetscBool PetscIsInfOrNanScalar(PetscScalar v) { return PetscIsInfOrNanReal(PetscAbsScalar(v)); } 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); /*@C PetscIsCloseAtTolScalar - Like `PetscIsCloseAtTol()` but for `PetscScalar` Input Parameters: + lhs - The first number . rhs - The second number . rtol - The relative tolerance - atol - The absolute tolerance Level: beginner Note: This routine is equivalent to `PetscIsCloseAtTol()` when PETSc is configured without complex numbers. .seealso: `PetscIsCloseAtTol()` @*/ static inline PetscBool PetscIsCloseAtTolScalar(PetscScalar lhs, PetscScalar rhs, PetscReal rtol, PetscReal atol) { PetscBool close = PetscIsCloseAtTol(PetscRealPart(lhs), PetscRealPart(rhs), rtol, atol); if (PetscDefined(USE_COMPLEX)) close = (PetscBool)(close && PetscIsCloseAtTol(PetscImaginaryPart(lhs), PetscImaginaryPart(rhs), rtol, atol)); return close; } /* 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 PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2scalar); /* MPI Datatypes for composite reductions */ struct petsc_mpiu_real_int { PetscReal v; PetscInt i; }; struct petsc_mpiu_scalar_int { PetscScalar v; PetscInt i; }; PETSC_EXTERN MPI_Datatype MPIU_REAL_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_real_int); PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_scalar_int); #if defined(PETSC_USE_64BIT_INDICES) struct /* __attribute__((packed, aligned(alignof(PetscInt *)))) */ petsc_mpiu_2int { PetscInt a; PetscInt b; }; struct __attribute__((packed)) petsc_mpiu_int_mpiint { PetscInt a; PetscMPIInt b; }; /* static_assert(sizeof(struct petsc_mpiu_2int) == 2 * sizeof(PetscInt), ""); static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt *), ""); static_assert(alignof(struct petsc_mpiu_2int) == alignof(PetscInt[2]), ""); clang generates warnings that petsc_mpiu_2int is not layout compatible with PetscInt[2] or PetscInt *, even though (with everything else uncommented) both of the static_asserts above pass! So we just comment it out... */ PETSC_EXTERN MPI_Datatype MPIU_2INT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_2int) */; PETSC_EXTERN MPI_Datatype MPIU_INT_MPIINT /* PETSC_ATTRIBUTE_MPI_TYPE_TAG_LAYOUT_COMPATIBLE(struct petsc_mpiu_int_mpiint) */; #else #define MPIU_2INT MPI_2INT #define MPIU_INT_MPIINT MPI_2INT #endif PETSC_EXTERN MPI_Datatype MPI_4INT; PETSC_EXTERN MPI_Datatype MPIU_4INT; static inline PetscInt PetscPowInt(PetscInt base, PetscInt power) { PetscInt result = 1; while (power) { if (power & 1) result *= base; power >>= 1; if (power) base *= base; } return result; } static inline PetscInt64 PetscPowInt64(PetscInt base, PetscInt power) { PetscInt64 result = 1; while (power) { if (power & 1) result *= base; power >>= 1; if (power) base *= base; } return result; } 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; if (power) base *= base; } return result; } 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; if (power) base *= base; } return result; } static inline PetscScalar PetscPowScalarReal(PetscScalar base, PetscReal power) { PetscScalar cpower = power; return PetscPowScalar(base, cpower); } /*MC PetscApproximateLTE - Performs a less than or equal to on a given constant with a fudge for floating point numbers Synopsis: #include bool PetscApproximateLTE(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 Level: advanced 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. Example\: .vb PetscReal x; if (PetscApproximateLTE(x, 3.2)) { // replaces if (x <= 3.2) { .ve .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateGTE()` M*/ #define PetscApproximateLTE(x, b) ((x) <= (PetscRealConstant(b) + PETSC_SMALL)) /*MC PetscApproximateGTE - Performs a greater than or equal to on a given constant with a fudge for floating point numbers Synopsis: #include bool PetscApproximateGTE(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 Level: advanced 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. Example\: .vb PetscReal x; if (PetscApproximateGTE(x, 3.2)) { // replaces if (x >= 3.2) { .ve .seealso: `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()` M*/ #define PetscApproximateGTE(x, b) ((x) >= (PetscRealConstant(b) - PETSC_SMALL)) /*@C PetscCeilInt - Returns the ceiling of the quotation of two positive integers Not Collective Input Parameters: + x - the numerator - y - the denominator Level: advanced Example\: .vb PetscInt n = PetscCeilInt(10, 3); // n has the value of 4 .ve .seealso: `PetscCeilInt64()`, `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()` @*/ static inline PetscInt PetscCeilInt(PetscInt x, PetscInt y) { return x / y + (x % y ? 1 : 0); } /*@C PetscCeilInt64 - Returns the ceiling of the quotation of two positive integers Not Collective Input Parameters: + x - the numerator - y - the denominator Level: advanced Example\: .vb PetscInt64 n = PetscCeilInt64(10, 3); // n has the value of 4 .ve .seealso: `PetscCeilInt()`, `PetscMax()`, `PetscMin()`, `PetscAbsInt()`, `PetscAbsReal()`, `PetscApproximateLTE()` @*/ static inline PetscInt64 PetscCeilInt64(PetscInt64 x, PetscInt64 y) { return x / y + (x % y ? 1 : 0); } PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt, const PetscReal[], const PetscReal[], PetscReal *, PetscReal *);