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/*
* qmath - declarations for extended precision rational arithmetic
*
* Copyright (C) 1999-2006 David I. Bell
*
* 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.
* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
*
* @(#) $Revision: 29.7 $
* @(#) $Id: qmath.h,v 29.7 2006/06/25 20:33:26 chongo Exp $
* @(#) $Source: /usr/local/src/cmd/calc/RCS/qmath.h,v $
*
* Under source code control: 1993/07/30 19:42:47
* File existed as early as: 1993
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
#if !defined(__QMATH_H__)
#define __QMATH_H__
#if defined(CALC_SRC) /* if we are building from the calc source tree */
# include "zmath.h"
#else
# include <calc/zmath.h>
#endif
#define INITCONSTCOUNT 9 /* number of initnumbs[] pre-defined constants */
/*
* Rational arithmetic definitions.
*/
struct number {
ZVALUE num; /* numerator (containing sign) */
ZVALUE den; /* denominator (always positive) */
long links; /* number of links to this value */
struct number *next; /* pointer to next number */
};
typedef struct number NUMBER;
extern NUMBER _qlge_;
/*
* Input. output, allocation, and conversion routines.
*/
extern NUMBER *qalloc(void);
extern NUMBER *qcopy(NUMBER *q);
extern NUMBER *uutoq(FULL i1, FULL i2);
extern NUMBER *iitoq(long i1, long i2);
extern NUMBER *str2q(char *str);
extern NUMBER *itoq(long i);
extern NUMBER *utoq(FULL i);
extern long qtoi(NUMBER *q);
extern FULL qtou(NUMBER *q);
extern long qparse(char *str, int flags);
extern void qfreenum(NUMBER *q);
extern void qprintnum(NUMBER *q, int mode);
extern void qprintff(NUMBER *q, long width, long precision);
extern void qprintfe(NUMBER *q, long width, long precision);
extern void qprintfr(NUMBER *q, long width, BOOL force);
extern void qprintfd(NUMBER *q, long width);
extern void qprintfx(NUMBER *q, long width);
extern void qprintfb(NUMBER *q, long width);
extern void qprintfo(NUMBER *q, long width);
extern void qprintf(char *, ...);
extern void shownumbers(void);
extern void showredcdata(void);
extern void freeredcdata(void);
extern void fitprint(NUMBER *, long);
/*
* Basic numeric routines.
*/
extern NUMBER *qaddi(NUMBER *q, long i);
extern NUMBER *qmuli(NUMBER *q, long i);
extern NUMBER *qdivi(NUMBER *q, long i);
extern NUMBER *qqadd(NUMBER *q1, NUMBER *q2);
extern NUMBER *qsub(NUMBER *q1, NUMBER *q2);
extern NUMBER *qmul(NUMBER *q1, NUMBER *q2);
extern NUMBER *qqdiv(NUMBER *q1, NUMBER *q2);
extern NUMBER *qquo(NUMBER *q1, NUMBER *q2, long rnd);
extern NUMBER *qmod(NUMBER *q1, NUMBER *q2, long rnd);
extern NUMBER *qmin(NUMBER *q1, NUMBER *q2);
extern NUMBER *qmax(NUMBER *q1, NUMBER *q2);
extern NUMBER *qand(NUMBER *q1, NUMBER *q2);
extern NUMBER *qor(NUMBER *q1, NUMBER *q2);
extern NUMBER *qxor(NUMBER *q1, NUMBER *q2);
extern NUMBER *qandnot(NUMBER *q1, NUMBER *q2);
extern NUMBER *qcomp(NUMBER *q);
extern NUMBER *qpowermod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
extern NUMBER *qpowi(NUMBER *q1, NUMBER *q2);
extern NUMBER *qsquare(NUMBER *q);
extern NUMBER *qneg(NUMBER *q);
extern NUMBER *qsign(NUMBER *q);
extern NUMBER *qint(NUMBER *q);
extern NUMBER *qfrac(NUMBER *q);
extern NUMBER *qnum(NUMBER *q);
extern NUMBER *qden(NUMBER *q);
extern NUMBER *qinv(NUMBER *q);
extern NUMBER *qqabs(NUMBER *q);
extern NUMBER *qinc(NUMBER *q);
extern NUMBER *qdec(NUMBER *q);
extern NUMBER *qshift(NUMBER *q, long n);
extern NUMBER *qtrunc(NUMBER *q1, NUMBER *q2);
extern NUMBER *qround(NUMBER *q, long places, long rnd);
extern NUMBER *qbtrunc(NUMBER *q1, NUMBER *q2);
extern NUMBER *qbround(NUMBER *q, long places, long rnd);
extern NUMBER *qscale(NUMBER *q, long i);
extern BOOL qdivides(NUMBER *q1, NUMBER *q2);
extern BOOL qcmp(NUMBER *q1, NUMBER *q2);
extern BOOL qcmpi(NUMBER *q, long i);
extern FLAG qrel(NUMBER *q1, NUMBER *q2);
extern FLAG qreli(NUMBER *q, long i);
extern BOOL qisset(NUMBER *q, long i);
/*
* More complicated numeric functions.
*/
extern NUMBER *qcomb(NUMBER *q1, NUMBER *q2);
extern NUMBER *qgcd(NUMBER *q1, NUMBER *q2);
extern NUMBER *qlcm(NUMBER *q1, NUMBER *q2);
extern NUMBER *qfact(NUMBER *q);
extern NUMBER *qpfact(NUMBER *q);
extern NUMBER *qminv(NUMBER *q1, NUMBER *q2);
extern NUMBER *qfacrem(NUMBER *q1, NUMBER *q2);
extern NUMBER *qperm(NUMBER *q1, NUMBER *q2);
extern NUMBER *qgcdrem(NUMBER *q1, NUMBER *q2);
extern NUMBER *qlowfactor(NUMBER *q1, NUMBER *q2);
extern NUMBER *qfib(NUMBER *q);
extern NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R);
extern NUMBER *qcfsim(NUMBER *q, long R);
extern NUMBER *qisqrt(NUMBER *q);
extern NUMBER *qjacobi(NUMBER *q1, NUMBER *q2);
extern NUMBER *qiroot(NUMBER *q1, NUMBER *q2);
extern NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
extern NUMBER *qlcmfact(NUMBER *q);
extern NUMBER *qredcin(NUMBER *q1, NUMBER *q2);
extern NUMBER *qredcout(NUMBER *q1, NUMBER *q2);
extern NUMBER *qredcmul(NUMBER *q1, NUMBER *q2, NUMBER *q3);
extern NUMBER *qredcsquare(NUMBER *q1, NUMBER *q2);
extern NUMBER *qredcpower(NUMBER *q1, NUMBER *q2, NUMBER *q3);
extern BOOL qprimetest(NUMBER *q1, NUMBER *q2, NUMBER *q3);
extern BOOL qissquare(NUMBER *q);
extern long qilog2(NUMBER *q);
extern long qilog10(NUMBER *q);
extern NUMBER *qilog(NUMBER *q, ZVALUE base);
extern BOOL qcmpmod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
extern BOOL qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod, long rnd);
extern FLAG qnear(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
extern NUMBER *qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base);
extern long qprecision(NUMBER *q);
extern long qplaces(NUMBER *q, ZVALUE base);
extern long qdecplaces(NUMBER *q);
extern long qdigits(NUMBER *q, ZVALUE base);
extern void setepsilon(NUMBER *q);
extern NUMBER *qbitvalue(long i);
extern NUMBER *qtenpow(long i);
/*
* Transcendental functions. These all take an epsilon argument to
* specify the required accuracy of the calculation.
*/
extern void qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc);
extern NUMBER *qsqrt(NUMBER *q, NUMBER *epsilon, long R);
extern NUMBER *qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
extern NUMBER *qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
extern NUMBER *qcos(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qsin(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qln(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qcsc(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacos(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qasin(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qatan(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qasec(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacsc(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacot(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qatan2(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
extern NUMBER *qhypot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
extern NUMBER *qcosh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qsinh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qtanh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qcoth(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qsech(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qcsch(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacosh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qasinh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qatanh(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qasech(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
extern NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, BOOL wantneg);
extern NUMBER *qpi(NUMBER *epsilon);
extern NUMBER *qcatalan(NUMBER *);
extern NUMBER *qbern(ZVALUE z);
extern void qfreebern(void);
extern NUMBER *qeuler(ZVALUE z);
extern void qfreeeuler(void);
/*
* pseudo-seed generator
*/
extern NUMBER *pseudo_seed(void);
/*
* external swap functions
*/
extern NUMBER *swap_b8_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
extern NUMBER *swap_b16_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
extern NUMBER *swap_HALF_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
/*
* macro expansions to speed this thing up
*/
#define qiszero(q) (ziszero((q)->num))
#define qisneg(q) (zisneg((q)->num))
#define qispos(q) (zispos((q)->num))
#define qisint(q) (zisunit((q)->den))
#define qisfrac(q) (!zisunit((q)->den))
#define qisunit(q) (zisunit((q)->num) && zisunit((q)->den))
#define qisone(q) (zisone((q)->num) && zisunit((q)->den))
#define qisnegone(q) (zisnegone((q)->num) && zisunit((q)->den))
#define qistwo(q) (zistwo((q)->num) && zisunit((q)->den))
#define qiseven(q) (zisunit((q)->den) && ziseven((q)->num))
#define qisodd(q) (zisunit((q)->den) && zisodd((q)->num))
#define qistwopower(q) (zisunit((q)->den) && zistwopower((q)->num))
#define qhighbit(q) (zhighbit((q)->num))
#define qlowbit(q) (zlowbit((q)->num))
#define qdivcount(q1, q2) (zdivcount((q1)->num, (q2)->num))
#define qlink(q) ((q)->links++, (q))
#define qfree(q) {if (--((q)->links) <= 0) qfreenum(q);}
/*
* Flags for qparse calls
*/
#define QPF_SLASH 0x1 /* allow slash for fractional number */
#define QPF_IMAG 0x2 /* allow trailing 'i' for imaginary number */
/*
* constants used often by the arithmetic routines
*/
extern NUMBER _qzero_, _qone_, _qnegone_, _qonehalf_, _qneghalf_, _qonesqbase_;
extern NUMBER _qtwo_, _qthree_, _qfour_, _qten_;
extern NUMBER * initnumbs[];
#endif /* !__QMATH_H__ */
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