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calc/cmath.h
Landon Curt Noll bf730f5518 add cmappr() and missing complex tan, cot, sec, csc in liblcac 
Added complex multiple approximation function to commath.c so
that users of libcalc may directly round complex number to
nearest multiple of a given real number:

    E_FUNC COMPLEX *cmappr(COMPLEX *c, NUMBER *e, long rnd, bool cfree);

For example:

    COMPLEX *c;             /* complex number to round to nearest epsilon */
    NUMBER *eps;            /* epsilon rounding precision */
    COMPLEX *res;           /* c rounded to nearest epsilon */
    long rnd = 24L;         /* a common rounding mode */
    bool ok_to_free;        /* true ==> free c, false ==> do not free c */

    ...

    res = cmappr(c, eps, ok_to_free);

The complex trigonometric functions tan, cot, sec, csc were implemented
in func.c as calls to complex sin and complex cos.  We added the
direct calls to comfunc.c so that users of libcalc may
call them directly:

    E_FUNC COMPLEX *c_tan(COMPLEX *c, NUMBER *eps);
    E_FUNC COMPLEX *c_cot(COMPLEX *c, NUMBER *eps);
    E_FUNC COMPLEX *c_sec(COMPLEX *c, NUMBER *eps);
    E_FUNC COMPLEX *c_cot(COMPLEX *c, NUMBER *eps);
2023-09-10 22:54:50 -07:00

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/*
* cmath - data structures for extended precision complex arithmetic
*
* Copyright (C) 1999-2007,2014,2023 David I. Bell and Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc 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 Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1993/07/30 19:42:45
* File existed as early as: 1993
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
#if !defined(INCLUDE_CMATH_H)
#define INCLUDE_CMATH_H
#if defined(CALC_SRC) /* if we are building from the calc source tree */
# include "qmath.h"
#else
# include <calc/qmath.h>
#endif
/*
* Complex arithmetic definitions.
*/
typedef struct {
NUMBER *real; /* real part of number */
NUMBER *imag; /* imaginary part of number */
long links; /* link count */
} COMPLEX;
/*
* Input, output, and conversion routines.
*/
E_FUNC COMPLEX *cmappr(COMPLEX *c, NUMBER *e, long rnd, bool cfree);
E_FUNC COMPLEX *comalloc(void);
E_FUNC COMPLEX *qqtoc(NUMBER *q1, NUMBER *q2);
E_FUNC void comfree(COMPLEX *c);
E_FUNC void comprint(COMPLEX *c);
E_FUNC void cprintfr(COMPLEX *c);
/*
* Basic numeric routines.
*/
E_FUNC COMPLEX *c_add(COMPLEX *c1, COMPLEX *c2);
E_FUNC COMPLEX *c_sub(COMPLEX *c1, COMPLEX *c2);
E_FUNC COMPLEX *c_mul(COMPLEX *c1, COMPLEX *c2);
E_FUNC COMPLEX *c_div(COMPLEX *c1, COMPLEX *c2);
E_FUNC COMPLEX *c_addq(COMPLEX *c, NUMBER *q);
E_FUNC COMPLEX *c_subq(COMPLEX *c, NUMBER *q);
E_FUNC COMPLEX *c_mulq(COMPLEX *c, NUMBER *q);
E_FUNC COMPLEX *c_divq(COMPLEX *c, NUMBER *q);
E_FUNC COMPLEX *c_scale(COMPLEX *c, long i);
E_FUNC COMPLEX *c_shift(COMPLEX *c, long i);
E_FUNC COMPLEX *c_square(COMPLEX *c);
E_FUNC COMPLEX *c_conj(COMPLEX *c);
E_FUNC COMPLEX *c_real(COMPLEX *c);
E_FUNC NUMBER *c_to_q(COMPLEX *c, bool cfree);
E_FUNC COMPLEX *c_imag(COMPLEX *c);
E_FUNC COMPLEX *c_neg(COMPLEX *c);
E_FUNC COMPLEX *c_inv(COMPLEX *c);
E_FUNC COMPLEX *c_int(COMPLEX *c);
E_FUNC COMPLEX *c_frac(COMPLEX *c);
E_FUNC bool c_cmp(COMPLEX *c1, COMPLEX *c2);
/*
* More complicated functions.
*/
E_FUNC COMPLEX *c_powi(COMPLEX *c, NUMBER *q);
E_FUNC NUMBER *c_ilog(COMPLEX *c, ZVALUE base);
/*
* Transcendental routines. These all take an epsilon argument to
* specify how accurately these are to be calculated.
*/
E_FUNC COMPLEX *c_power(COMPLEX *c1, COMPLEX *c2, NUMBER *epsilon);
E_FUNC COMPLEX *c_sqrt(COMPLEX *c, NUMBER *epsilon, long R);
E_FUNC COMPLEX *c_root(COMPLEX *c, NUMBER *q, NUMBER *epsilon);
E_FUNC COMPLEX *c_exp(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_ln(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_log(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_log2(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_cos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_sin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_cosh(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_sinh(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_polar(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC COMPLEX *c_rel(COMPLEX *c1, COMPLEX *c2);
E_FUNC COMPLEX *c_asin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_tan(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_atan(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_cot(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acot(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_sec(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_asec(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_csc(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acsc(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_asinh(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acosh(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_atanh(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acoth(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_asech(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acsch(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_gd(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_agd(COMPLEX *c, NUMBER *epsilon);
/*
* historical trig functions
*/
E_FUNC COMPLEX *c_versin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_aversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_coversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acoversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_vercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_avercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_covercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acovercos(COMPLEX *c, NUMBER *epsilon);
/*
* external functions
*/
E_FUNC COMPLEX *swap_b8_in_COMPLEX(COMPLEX *dest, COMPLEX *src, bool all);
E_FUNC COMPLEX *swap_b16_in_COMPLEX(COMPLEX *dest, COMPLEX *src, bool all);
E_FUNC COMPLEX *swap_HALF_in_COMPLEX(COMPLEX *dest, COMPLEX *src, bool all);
/*
* macro expansions to speed this thing up
*/
#define cisreal(c) (qiszero((c)->imag))
#define cisimag(c) (qiszero((c)->real) && !cisreal(c))
#define ciszero(c) (cisreal(c) && qiszero((c)->real))
#define cisone(c) (cisreal(c) && qisone((c)->real))
#define cisnegone(c) (cisreal(c) && qisnegone((c)->real))
#define cisrunit(c) (cisreal(c) && qisunit((c)->real))
#define cisiunit(c) (qiszero((c)->real) && qisunit((c)->imag))
#define cisunit(c) (cisrunit(c) || cisiunit(c))
#define cistwo(c) (cisreal(c) && qistwo((c)->real))
#define cisint(c) (qisint((c)->real) && qisint((c)->imag))
#define ciseven(c) (qiseven((c)->real) && qiseven((c)->imag))
#define cisodd(c) (qisodd((c)->real) || qisodd((c)->imag))
#define clink(c) ((c)->links++, (c))
/*
* Pre-defined values.
*/
EXTERN COMPLEX _czero_, _cone_, _conei_;
#endif /* !INCLUDE_CMATH_H */
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