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|
/*@@
@file Complex.c
@date Tue Dec 14 12:09:43 1999
@author Tom Goodale
@desc
Complex variable stuff
@enddesc
@version $Id$
@@*/
#include <complex.h>
#include <math.h>
#include "cctk_Flesh.h"
#ifndef DEFINE_CCTK_COMPLEX_INLINE_FUNCTIONS
# define DEFINE_CCTK_COMPLEX_EXTERN_FUNCTIONS
# include "cctk_Complex.h"
# undef DEFINE_CCTK_COMPLEX_EXTERN_FUNCTIONS
#endif
#ifndef DEFINE_CCTK_COMPLEX_INLINE_FUNCTIONS
static const char *rcsid = "$Header$";
CCTK_FILEVERSION(main_Complex_c);
#endif
/********************************************************************
********************* Local Data Types ***********************
********************************************************************/
/********************************************************************
********************* Local Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Other Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Local Data *****************************
********************************************************************/
/********************************************************************
********************* External Routines **********************
********************************************************************/
/*@@
@routine CCTK_Cmplx
@date Tue Dec 14 12:16:01 1999
@author Tom Goodale
@desc
Turns two reals into a complex number
@enddesc
@var Re
@vdesc Real part
@vtype CCTK_REAL
@vio in
@endvar
@var Im
@vdesc Imaginary part
@vtype CCTK_REAL
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx (cctk_real Re, cctk_real Im) \
{ \
return Re + _Complex_I * Im; \
}
/*@@
@routine CCTK_CmplxReal
@date Tue Dec 14 12:22:41 1999
@author Tom Goodale
@desc
Returns the real part of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_REAL
@returndesc
The real part
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_REAL(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_real CCTK_Cmplx##Real (cctk_complex x) \
{ \
return creal##type(x); \
}
/*@@
@routine CCTK_CmplxImag
@date Tue Dec 14 12:22:41 1999
@author Tom Goodale
@desc
Returns the imaginary part of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_REAL
@returndesc
The imaginary part
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_IMAG(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_real CCTK_Cmplx##Imag (cctk_complex x) \
{ \
return cimag##type(x); \
}
/*@@
@routine CCTK_CmplxNeg
@date 2006-06-07
@author Erik Schnetter
@desc
Returns the negative of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The negative
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_NEG(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Neg (cctk_complex x) \
{ \
return -x; \
}
/*@@
@routine CCTK_CmplxConjg
@date Tue Dec 14 12:22:41 1999
@author Tom Goodale
@desc
Returns the complex conjugate of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The complex conjugate
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_CONJG(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Conjg (cctk_complex x) \
{ \
return conj##type(x); \
}
/*@@
@routine CCTK_CmplxAbs
@date Tue Dec 14 12:26:33 1999
@author Tom Goodale
@desc
Return the absolute value of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_REAL
@returndesc
The absolute value of the complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_ABS(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_real CCTK_Cmplx##Abs (cctk_complex x) \
{ \
return cabs##type(x); \
}
/*@@
@routine CCTK_CmplxNorm
@date 2006-07-06
@author Erik Schnetter
@desc
Return the absolute value squared of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_REAL
@returndesc
The absolute value squared of the complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_NORM(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_real CCTK_Cmplx##Norm (cctk_complex x) \
{ \
return creal##type(x)*creal##type(x) + cimag##type(x)*cimag##type(x); \
}
/*@@
@routine CCTK_CmplxArg
@date 2005-11-17
@author Erik Schnetter
@desc
Return the argument of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_REAL
@returndesc
The argument of the complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_ARG(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_real CCTK_Cmplx##Arg (cctk_complex x) \
{ \
return carg##type(x); \
}
/*@@
@routine CCTK_CmplxAdd
@date Sat Dec 4 12:11:04 1999
@author Gabrielle Allen
@desc
Adds two complex numbers
@enddesc
@var a
@vdesc First summand
@vtype CCTK_COMPLEX
@vio in
@endvar
@var b
@vdesc Second summand
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The sum of a and b
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_ADD(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Add (cctk_complex a, cctk_complex b) \
{ \
return a+b; \
}
/*@@
@routine CCTK_CmplxSub
@date Sat Dec 4 12:11:04 1999
@author Gabrielle Allen
@desc
Subtracts two complex numbers
@enddesc
@var a
@vdesc First operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@var b
@vdesc Second operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The difference
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_SUB(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Sub (cctk_complex a, cctk_complex b) \
{ \
return a-b; \
}
/*@@
@routine CCTK_CmplxMul
@date Sat Dec 4 12:11:04 1999
@author Gabrielle Allen
@desc
Multiplies two complex numbers
@enddesc
@var a
@vdesc First operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@var b
@vdesc Second operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The product
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_MUL(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Mul (cctk_complex a, cctk_complex b) \
{ \
return a*b; \
}
/*@@
@routine CCTK_CmplxDiv
@date Sat Dec 4 12:11:04 1999
@author Gabrielle Allen
@desc
Divide two complex numbers.
@enddesc
@var a
@vdesc First operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@var b
@vdesc Second operand
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The quotient
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_DIV(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Div (cctk_complex a, cctk_complex b) \
{ \
return a/b; \
}
/*@@
@routine CCTK_CmplxCPow
@date 2005-11-17
@author Erik Schnetter
@desc
Raises a complex number to a given power
@enddesc
@var a
@vdesc The base
@vtype CCTK_COMPLEX
@vio in
@endvar
@var b
@vdesc The exponent
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
a to the power of b
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_CPOW(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##CPow (cctk_complex a, cctk_complex b) \
{ \
return cpow##type(a, b); \
}
/*@@
@routine CCTK_CmplxSin
@date Wed 12 Dec 2001
@author Thomas Radke
@desc
Returns the sine of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The sine
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_SIN(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Sin (cctk_complex x) \
{ \
return csin##type(x); \
}
/*@@
@routine CCTK_CmplxCos
@date Wed 12 Dec 2001
@author Thomas Radke
@desc
Returns the cosine of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The cosine
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_COS(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Cos (cctk_complex x) \
{ \
return ccos##type(x); \
}
/*@@
@routine CCTK_CmplxExp
@date Wed 12 Dec 2001
@author Thomas Radke
@desc
Returns the exponential of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The exponential
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_EXP(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Exp (cctk_complex x) \
{ \
return cexp##type(x); \
}
/*@@
@routine CCTK_CmplxLog
@date 2005-11-17
@author Erik Schnetter
@desc
Returns the logarithm of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The logarithm
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_LOG(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Log (cctk_complex x) \
{ \
return clog##type(x); \
}
/*@@
@routine CCTK_CmplxSqrt
@date Wed 12 Dec 2001
@author Thomas Radke
@desc
Returns the square root of a complex number.
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The square root
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_SQRT(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Sqrt (cctk_complex x) \
{ \
return csqrt##type(x); \
}
/*@@
@routine CCTK_CmplxPow
@date
@author Yaakoub Y El Khamra
@desc
Raises a complex number to a given power
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@var w
@vdesc The exponent
@vtype CCTK_REAL
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The power of the complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_POW(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##Pow (cctk_complex x, cctk_real w) \
{ \
return cpow##type(x, w); \
}
/*@@
@routine CCTK_CmplxIPow
@date
@author Erik Schnetter
@desc
Raises a complex number to a given power
@enddesc
@var x
@vdesc The complex number
@vtype CCTK_COMPLEX
@vio in
@endvar
@var w
@vdesc The exponent
@vtype int
@vio in
@endvar
@returntype CCTK_COMPLEX
@returndesc
The power of the complex number
@endreturndesc
@@*/
#define DEFINE_CCTK_CMPLX_IPOW(CCTK_Cmplx, cctk_real, cctk_complex, type) \
cctk_complex CCTK_Cmplx##IPow (cctk_complex x, int w) \
{ \
int w0 = w; \
cctk_complex result = 1; \
while (w) \
{ \
if (w % 2) \
{ \
result *= x; \
} \
w /= 2; \
x *= x; \
} \
if (w0 < 0) \
{ \
result = 1 / result; \
} \
return result; \
}
/* macro to define a set of complex functions for a given precision */
#define DEFINE_CMPLX_FUNCTIONS(CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_REAL (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_IMAG (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_NEG (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_CONJG (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_ABS (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_NORM (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_ARG (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_ADD (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_SUB (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_MUL (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_DIV (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_CPOW (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_SIN (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_COS (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_EXP (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_LOG (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_SQRT (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_POW (CCTK_Cmplx, cctk_real, cctk_complex, type) \
DEFINE_CCTK_CMPLX_IPOW (CCTK_Cmplx, cctk_real, cctk_complex, type)
/* define complex functions for all available precisions */
#ifdef HAVE_CCTK_REAL4
#define KIND_SUFFIX f
DEFINE_CMPLX_FUNCTIONS (CCTK_Cmplx8, CCTK_REAL4, CCTK_COMPLEX8, KIND_SUFFIX)
#undef KIND_SUFFIX
#endif
#ifdef HAVE_CCTK_REAL8
#define KIND_SUFFIX
DEFINE_CMPLX_FUNCTIONS (CCTK_Cmplx16, CCTK_REAL8, CCTK_COMPLEX16, KIND_SUFFIX)
#undef KIND_SUFFIX
#endif
#ifdef HAVE_CCTK_REAL16
#define KIND_SUFFIX l
DEFINE_CMPLX_FUNCTIONS (CCTK_Cmplx32, CCTK_REAL16, CCTK_COMPLEX32, KIND_SUFFIX)
#undef KIND_SUFFIX
#endif
|
