funcs.h

A C++ class library for scientific computing

// -*- C++ -*-
/***************************************************************************
 * blitz/funcs.h            Function objects for math functions
 *
 * $Id: funcs.h,v 1.7 2005/10/08 01:22:55 julianc Exp $
 *
 * Copyright (C) 1997-2001 Todd Veldhuizen <[e-mail]>
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * Suggestions:          [e-mail]
 * Bugs:                 [e-mail]
 *
 * For more information, please see the Blitz++ Home Page:
 *    http://oonumerics.org/blitz/
 *
 *************************************************************************/

#ifndef BZ_FUNCS_H
#define BZ_FUNCS_H

#include <blitz/blitz.h>
#include <blitz/promote.h>
#include <blitz/prettyprint.h>

BZ_NAMESPACE(blitz)
    
/* Helper functions */
    
template <typename T>
inline T blitz_sqr(T x)
{ return x*x; }

template <typename T>
inline T blitz_cube(T x)
{ return x*x*x; }

template <typename T>
inline T blitz_pow4(T x)
{ return x*x*x*x; }

template <typename T>
inline T blitz_pow5(T x)
{ return x*x*x*x*x; }

template <typename T>
inline T blitz_pow6(T x)
{ return x*x*x*x*x*x; }

template <typename T>
inline T blitz_pow7(T x)
{ return x*x*x*x*x*x*x; }

template <typename T>
inline T blitz_pow8(T x)
{ return x*x*x*x*x*x*x*x; }


/* Unary functions that return same type as argument */
    
#define BZ_DEFINE_UNARY_FUNC(name,fun)                         \
template<typename T_numtype1>                                  \
struct name {                                                  \
    typedef T_numtype1 T_numtype;                              \
                                                               \
    static inline T_numtype                                    \
    apply(T_numtype1 a)                                        \
    { return fun(a); }                                         \
							       \
    template<typename T1>                                      \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,  \
        prettyPrintFormat& format, const T1& t1)               \
    {                                                          \
        str += #fun;                                           \
        str += "(";                                            \
        t1.prettyPrint(str, format);                           \
        str += ")";                                            \
    }                                                          \
};

BZ_DEFINE_UNARY_FUNC(Fn_acos,BZ_MATHFN_SCOPE(acos))
BZ_DEFINE_UNARY_FUNC(Fn_asin,BZ_MATHFN_SCOPE(asin))
BZ_DEFINE_UNARY_FUNC(Fn_atan,BZ_MATHFN_SCOPE(atan))
BZ_DEFINE_UNARY_FUNC(Fn_ceil,BZ_MATHFN_SCOPE(ceil))
BZ_DEFINE_UNARY_FUNC(Fn_cos,BZ_MATHFN_SCOPE(cos))
BZ_DEFINE_UNARY_FUNC(Fn_cosh,BZ_MATHFN_SCOPE(cosh))
BZ_DEFINE_UNARY_FUNC(Fn_exp,BZ_MATHFN_SCOPE(exp))
BZ_DEFINE_UNARY_FUNC(Fn_fabs,BZ_MATHFN_SCOPE(fabs))
BZ_DEFINE_UNARY_FUNC(Fn_floor,BZ_MATHFN_SCOPE(floor))
BZ_DEFINE_UNARY_FUNC(Fn_log,BZ_MATHFN_SCOPE(log))
BZ_DEFINE_UNARY_FUNC(Fn_log10,BZ_MATHFN_SCOPE(log10))
BZ_DEFINE_UNARY_FUNC(Fn_sin,BZ_MATHFN_SCOPE(sin))
BZ_DEFINE_UNARY_FUNC(Fn_sinh,BZ_MATHFN_SCOPE(sinh))
BZ_DEFINE_UNARY_FUNC(Fn_sqrt,BZ_MATHFN_SCOPE(sqrt))
BZ_DEFINE_UNARY_FUNC(Fn_tan,BZ_MATHFN_SCOPE(tan))
BZ_DEFINE_UNARY_FUNC(Fn_tanh,BZ_MATHFN_SCOPE(tanh))

#ifdef BZ_HAVE_IEEE_MATH
BZ_DEFINE_UNARY_FUNC(Fn_acosh,BZ_IEEEMATHFN_SCOPE(acosh))
BZ_DEFINE_UNARY_FUNC(Fn_asinh,BZ_IEEEMATHFN_SCOPE(asinh))
BZ_DEFINE_UNARY_FUNC(Fn_atanh,BZ_IEEEMATHFN_SCOPE(atanh))
BZ_DEFINE_UNARY_FUNC(Fn_cbrt,BZ_IEEEMATHFN_SCOPE(cbrt))
BZ_DEFINE_UNARY_FUNC(Fn_erf,BZ_IEEEMATHFN_SCOPE(erf))
BZ_DEFINE_UNARY_FUNC(Fn_erfc,BZ_IEEEMATHFN_SCOPE(erfc))
BZ_DEFINE_UNARY_FUNC(Fn_expm1,BZ_IEEEMATHFN_SCOPE(expm1))
BZ_DEFINE_UNARY_FUNC(Fn_j0,BZ_IEEEMATHFN_SCOPE(j0))
BZ_DEFINE_UNARY_FUNC(Fn_j1,BZ_IEEEMATHFN_SCOPE(j1))
BZ_DEFINE_UNARY_FUNC(Fn_lgamma,BZ_IEEEMATHFN_SCOPE(lgamma))
BZ_DEFINE_UNARY_FUNC(Fn_logb,BZ_IEEEMATHFN_SCOPE(logb))
BZ_DEFINE_UNARY_FUNC(Fn_log1p,BZ_IEEEMATHFN_SCOPE(log1p))
BZ_DEFINE_UNARY_FUNC(Fn_rint,BZ_IEEEMATHFN_SCOPE(rint))
BZ_DEFINE_UNARY_FUNC(Fn_y0,BZ_IEEEMATHFN_SCOPE(y0))
BZ_DEFINE_UNARY_FUNC(Fn_y1,BZ_IEEEMATHFN_SCOPE(y1))
#endif
    
#ifdef BZ_HAVE_SYSTEM_V_MATH
BZ_DEFINE_UNARY_FUNC(Fn__class,BZ_IEEEMATHFN_SCOPE(_class))
BZ_DEFINE_UNARY_FUNC(Fn_nearest,BZ_IEEEMATHFN_SCOPE(nearest))
BZ_DEFINE_UNARY_FUNC(Fn_rsqrt,BZ_IEEEMATHFN_SCOPE(rsqrt))
#endif
    
BZ_DEFINE_UNARY_FUNC(Fn_sqr,BZ_BLITZ_SCOPE(blitz_sqr))
BZ_DEFINE_UNARY_FUNC(Fn_cube,BZ_BLITZ_SCOPE(blitz_cube))
BZ_DEFINE_UNARY_FUNC(Fn_pow4,BZ_BLITZ_SCOPE(blitz_pow4))
BZ_DEFINE_UNARY_FUNC(Fn_pow5,BZ_BLITZ_SCOPE(blitz_pow5))
BZ_DEFINE_UNARY_FUNC(Fn_pow6,BZ_BLITZ_SCOPE(blitz_pow6))
BZ_DEFINE_UNARY_FUNC(Fn_pow7,BZ_BLITZ_SCOPE(blitz_pow7))
BZ_DEFINE_UNARY_FUNC(Fn_pow8,BZ_BLITZ_SCOPE(blitz_pow8))

/* Unary functions that return a specified type */
    
#define BZ_DEFINE_UNARY_FUNC_RET(name,fun,ret)                 \
template<typename T_numtype1>                                  \
struct name {                                                  \
    typedef ret T_numtype;                                     \
                                                               \
    static inline T_numtype                                    \
    apply(T_numtype1 a)                                        \
    { return fun(a); }                                         \
							       \
    template<typename T1>                                      \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,  \
        prettyPrintFormat& format, const T1& t1)               \
    {                                                          \
        str += #fun;                                           \
        str += "(";                                            \
        t1.prettyPrint(str, format);                           \
        str += ")";                                            \
    }                                                          \
};

#ifdef BZ_HAVE_IEEE_MATH
BZ_DEFINE_UNARY_FUNC_RET(Fn_ilogb,BZ_IEEEMATHFN_SCOPE(ilogb),int)
#endif
    
#ifdef BZ_HAVE_SYSTEM_V_MATH
BZ_DEFINE_UNARY_FUNC_RET(Fn_itrunc,BZ_IEEEMATHFN_SCOPE(itrunc),int)
BZ_DEFINE_UNARY_FUNC_RET(Fn_uitrunc,BZ_IEEEMATHFN_SCOPE(uitrunc),unsigned int)
#endif
    
    
#ifdef BZ_HAVE_COMPLEX
/* Specialization of unary functor for complex type */
    
#define BZ_DEFINE_UNARY_CFUNC(name,fun)                        \
template<typename T>                                           \
struct name< complex<T> > {                                    \
    typedef complex<T> T_numtype1;                             \
    typedef complex<T> T_numtype;                              \
                                                               \
    static inline T_numtype                                    \
    apply(T_numtype1 a)                                        \
    { return fun(a); }                                         \
							       \
    template<typename T1>                                      \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,  \
        prettyPrintFormat& format, const T1& t1)               \
    {                                                          \
        str += #fun;                                           \
        str += "(";                                            \
        t1.prettyPrint(str, format);                           \
        str += ")";                                            \
    }                                                          \
};

#ifdef BZ_HAVE_COMPLEX_FCNS
BZ_DEFINE_UNARY_FUNC(Fn_conj,BZ_CMATHFN_SCOPE(conj))
#endif

#ifdef BZ_HAVE_COMPLEX_MATH1
BZ_DEFINE_UNARY_CFUNC(Fn_cos,BZ_CMATHFN_SCOPE(cos))
BZ_DEFINE_UNARY_CFUNC(Fn_cosh,BZ_CMATHFN_SCOPE(cosh))
BZ_DEFINE_UNARY_CFUNC(Fn_exp,BZ_CMATHFN_SCOPE(exp))
BZ_DEFINE_UNARY_CFUNC(Fn_log,BZ_CMATHFN_SCOPE(log))
BZ_DEFINE_UNARY_CFUNC(Fn_log10,BZ_CMATHFN_SCOPE(log10))
BZ_DEFINE_UNARY_CFUNC(Fn_sin,BZ_CMATHFN_SCOPE(sin))
BZ_DEFINE_UNARY_CFUNC(Fn_sinh,BZ_CMATHFN_SCOPE(sinh))
BZ_DEFINE_UNARY_CFUNC(Fn_sqrt,BZ_CMATHFN_SCOPE(sqrt))
BZ_DEFINE_UNARY_CFUNC(Fn_tan,BZ_CMATHFN_SCOPE(tan))
BZ_DEFINE_UNARY_CFUNC(Fn_tanh,BZ_CMATHFN_SCOPE(tanh))
#endif // BZ_HAVE_COMPLEX_MATH1

BZ_DEFINE_UNARY_CFUNC(Fn_sqr,BZ_BLITZ_SCOPE(blitz_sqr))
BZ_DEFINE_UNARY_CFUNC(Fn_cube,BZ_BLITZ_SCOPE(blitz_cube))
BZ_DEFINE_UNARY_CFUNC(Fn_pow4,BZ_BLITZ_SCOPE(blitz_pow4))
BZ_DEFINE_UNARY_CFUNC(Fn_pow5,BZ_BLITZ_SCOPE(blitz_pow5))
BZ_DEFINE_UNARY_CFUNC(Fn_pow6,BZ_BLITZ_SCOPE(blitz_pow6))
BZ_DEFINE_UNARY_CFUNC(Fn_pow7,BZ_BLITZ_SCOPE(blitz_pow7))
BZ_DEFINE_UNARY_CFUNC(Fn_pow8,BZ_BLITZ_SCOPE(blitz_pow8))

/* Unary functions that apply only to complex<T> and return T */
    
#define BZ_DEFINE_UNARY_CFUNC2(name,fun)                       \
template<typename T_numtype1>                                  \
struct name;                                                   \
                                                               \
template<typename T>                                           \
struct name< complex<T> > {                                    \
    typedef complex<T> T_numtype1;                             \
    typedef T T_numtype;                                       \
                                                               \
    static inline T_numtype                                    \
    apply(T_numtype1 a)                                        \
    { return fun(a); }                                         \
							       \
    template<typename T1>                                      \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,  \
        prettyPrintFormat& format, const T1& t1)               \
    {                                                          \
        str += #fun;                                           \
        str += "(";                                            \
        t1.prettyPrint(str, format);                           \
        str += ")";                                            \
    }                                                          \
};

#ifdef BZ_HAVE_COMPLEX_FCNS
BZ_DEFINE_UNARY_CFUNC2(Fn_arg,BZ_CMATHFN_SCOPE(arg))
BZ_DEFINE_UNARY_CFUNC2(Fn_imag,BZ_CMATHFN_SCOPE(imag))
BZ_DEFINE_UNARY_CFUNC2(Fn_norm,BZ_CMATHFN_SCOPE(norm))
BZ_DEFINE_UNARY_CFUNC2(Fn_real,BZ_CMATHFN_SCOPE(real))
#endif // BZ_HAVE_COMPLEX_FCNS
    
#endif // BZ_HAVE_COMPLEX
    
/* Binary functions that return type based on type promotion */
    
#define BZ_DEFINE_BINARY_FUNC(name,fun)                           \
template<typename T_numtype1, typename T_numtype2>                \
struct name {                                                     \
    typedef BZ_PROMOTE(T_numtype1, T_numtype2) T_numtype;         \
                                                                  \
    static inline T_numtype                                       \
    apply(T_numtype1 a, T_numtype2 b)                             \
    { return fun(a,b); }                                          \
							          \
    template<typename T1, typename T2>                            \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,     \
        prettyPrintFormat& format, const T1& t1,                  \
        const T2& t2)                                             \
    {                                                             \
        str += #fun;                                              \
        str += "(";                                               \
        t1.prettyPrint(str, format);                              \
        str += ",";                                               \
        t2.prettyPrint(str, format);                              \
        str += ")";                                               \
    }                                                             \
};

BZ_DEFINE_BINARY_FUNC(Fn_atan2,BZ_MATHFN_SCOPE(atan2))
BZ_DEFINE_BINARY_FUNC(Fn_fmod,BZ_MATHFN_SCOPE(fmod))
BZ_DEFINE_BINARY_FUNC(Fn_pow,BZ_MATHFN_SCOPE(pow))
    
#ifdef BZ_HAVE_SYSTEM_V_MATH
BZ_DEFINE_BINARY_FUNC(Fn_copysign,BZ_IEEEMATHFN_SCOPE(copysign))
BZ_DEFINE_BINARY_FUNC(Fn_drem,BZ_IEEEMATHFN_SCOPE(drem))
BZ_DEFINE_BINARY_FUNC(Fn_hypot,BZ_IEEEMATHFN_SCOPE(hypot))
BZ_DEFINE_BINARY_FUNC(Fn_nextafter,BZ_IEEEMATHFN_SCOPE(nextafter))
BZ_DEFINE_BINARY_FUNC(Fn_remainder,BZ_IEEEMATHFN_SCOPE(remainder))
BZ_DEFINE_BINARY_FUNC(Fn_scalb,BZ_IEEEMATHFN_SCOPE(scalb))
#endif
    
/* Binary functions that return a specified type */
    
#define BZ_DEFINE_BINARY_FUNC_RET(name,fun,ret)                   \
template<typename T_numtype1, typename T_numtype2>                \
struct name {                                                     \
    typedef ret T_numtype;                                        \
                                                                  \
    static inline T_numtype                                       \
    apply(T_numtype1 a, T_numtype2 b)                             \
    { return fun(a,b); }                                          \
							          \
    template<typename T1, typename T2>                            \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,     \
        prettyPrintFormat& format, const T1& t1,                  \
        const T2& t2)                                             \
    {                                                             \
        str += #fun;                                              \
        str += "(";                                               \
        t1.prettyPrint(str, format);                              \
        str += ",";                                               \
        t2.prettyPrint(str, format);                              \
        str += ")";                                               \
    }                                                             \
};

#ifdef BZ_HAVE_SYSTEM_V_MATH
BZ_DEFINE_BINARY_FUNC_RET(Fn_unordered,BZ_IEEEMATHFN_SCOPE(unordered),int)
#endif
    
#ifdef BZ_HAVE_COMPLEX
/* Specialization of binary functor for complex type */
    
#define BZ_DEFINE_BINARY_CFUNC(name,fun)                       \
template<typename T>                                           \
struct name< complex<T>, complex<T> > {                        \
    typedef complex<T> T_numtype1;                             \
    typedef complex<T> T_numtype2;                             \
    typedef complex<T> T_numtype;                              \
                                                               \
    static inline T_numtype                                    \
    apply(T_numtype1 a, T_numtype2 b)                          \
    { return fun(a,b); }                                       \
							       \
    template<typename T1, typename T2>                         \
    static inline void prettyPrint(BZ_STD_SCOPE(string) &str,  \
        prettyPrintFormat& format, const T1& t1,               \
        const T2& t2)                                          \
    {                                                          \
        str += #fun;                                           \
        str += "(";                                            \
        t1.prettyPrint(str, format);                           \