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278 lines
9.9 KiB
C
278 lines
9.9 KiB
C
/*
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* qmath - declarations for extended precision rational arithmetic
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*
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* Copyright (C) 1999-2006 David I. Bell
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
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*
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* @(#) $Revision: 29.7 $
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* @(#) $Id: qmath.h,v 29.7 2006/06/25 20:33:26 chongo Exp $
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* @(#) $Source: /usr/local/src/cmd/calc/RCS/qmath.h,v $
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*
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* Under source code control: 1993/07/30 19:42:47
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* File existed as early as: 1993
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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#if !defined(__QMATH_H__)
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#define __QMATH_H__
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#if defined(CALC_SRC) /* if we are building from the calc source tree */
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# include "zmath.h"
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#else
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# include <calc/zmath.h>
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#endif
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#define INITCONSTCOUNT 9 /* number of initnumbs[] pre-defined constants */
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/*
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* Rational arithmetic definitions.
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*/
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struct number {
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ZVALUE num; /* numerator (containing sign) */
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ZVALUE den; /* denominator (always positive) */
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long links; /* number of links to this value */
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struct number *next; /* pointer to next number */
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};
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typedef struct number NUMBER;
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extern NUMBER _qlge_;
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/*
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* Input. output, allocation, and conversion routines.
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*/
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extern NUMBER *qalloc(void);
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extern NUMBER *qcopy(NUMBER *q);
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extern NUMBER *uutoq(FULL i1, FULL i2);
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extern NUMBER *iitoq(long i1, long i2);
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extern NUMBER *str2q(char *str);
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extern NUMBER *itoq(long i);
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extern NUMBER *utoq(FULL i);
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extern long qtoi(NUMBER *q);
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extern FULL qtou(NUMBER *q);
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extern long qparse(char *str, int flags);
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extern void qfreenum(NUMBER *q);
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extern void qprintnum(NUMBER *q, int mode);
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extern void qprintff(NUMBER *q, long width, long precision);
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extern void qprintfe(NUMBER *q, long width, long precision);
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extern void qprintfr(NUMBER *q, long width, BOOL force);
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extern void qprintfd(NUMBER *q, long width);
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extern void qprintfx(NUMBER *q, long width);
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extern void qprintfb(NUMBER *q, long width);
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extern void qprintfo(NUMBER *q, long width);
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extern void qprintf(char *, ...);
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extern void shownumbers(void);
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extern void showredcdata(void);
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extern void freeredcdata(void);
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extern void fitprint(NUMBER *, long);
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/*
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* Basic numeric routines.
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*/
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extern NUMBER *qaddi(NUMBER *q, long i);
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extern NUMBER *qmuli(NUMBER *q, long i);
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extern NUMBER *qdivi(NUMBER *q, long i);
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extern NUMBER *qqadd(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qsub(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qmul(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qqdiv(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qquo(NUMBER *q1, NUMBER *q2, long rnd);
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extern NUMBER *qmod(NUMBER *q1, NUMBER *q2, long rnd);
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extern NUMBER *qmin(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qmax(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qand(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qor(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qxor(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qandnot(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qcomp(NUMBER *q);
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extern NUMBER *qpowermod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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extern NUMBER *qpowi(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qsquare(NUMBER *q);
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extern NUMBER *qneg(NUMBER *q);
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extern NUMBER *qsign(NUMBER *q);
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extern NUMBER *qint(NUMBER *q);
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extern NUMBER *qfrac(NUMBER *q);
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extern NUMBER *qnum(NUMBER *q);
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extern NUMBER *qden(NUMBER *q);
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extern NUMBER *qinv(NUMBER *q);
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extern NUMBER *qqabs(NUMBER *q);
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extern NUMBER *qinc(NUMBER *q);
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extern NUMBER *qdec(NUMBER *q);
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extern NUMBER *qshift(NUMBER *q, long n);
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extern NUMBER *qtrunc(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qround(NUMBER *q, long places, long rnd);
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extern NUMBER *qbtrunc(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qbround(NUMBER *q, long places, long rnd);
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extern NUMBER *qscale(NUMBER *q, long i);
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extern BOOL qdivides(NUMBER *q1, NUMBER *q2);
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extern BOOL qcmp(NUMBER *q1, NUMBER *q2);
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extern BOOL qcmpi(NUMBER *q, long i);
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extern FLAG qrel(NUMBER *q1, NUMBER *q2);
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extern FLAG qreli(NUMBER *q, long i);
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extern BOOL qisset(NUMBER *q, long i);
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/*
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* More complicated numeric functions.
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*/
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extern NUMBER *qcomb(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qgcd(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qlcm(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qfact(NUMBER *q);
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extern NUMBER *qpfact(NUMBER *q);
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extern NUMBER *qminv(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qfacrem(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qperm(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qgcdrem(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qlowfactor(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qfib(NUMBER *q);
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extern NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R);
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extern NUMBER *qcfsim(NUMBER *q, long R);
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extern NUMBER *qisqrt(NUMBER *q);
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extern NUMBER *qjacobi(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qiroot(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
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extern NUMBER *qlcmfact(NUMBER *q);
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extern NUMBER *qredcin(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qredcout(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qredcmul(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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extern NUMBER *qredcsquare(NUMBER *q1, NUMBER *q2);
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extern NUMBER *qredcpower(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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extern BOOL qprimetest(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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extern BOOL qissquare(NUMBER *q);
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extern long qilog2(NUMBER *q);
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extern long qilog10(NUMBER *q);
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extern NUMBER *qilog(NUMBER *q, ZVALUE base);
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extern BOOL qcmpmod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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extern BOOL qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod, long rnd);
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extern FLAG qnear(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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extern NUMBER *qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base);
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extern long qprecision(NUMBER *q);
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extern long qplaces(NUMBER *q, ZVALUE base);
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extern long qdecplaces(NUMBER *q);
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extern long qdigits(NUMBER *q, ZVALUE base);
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extern void setepsilon(NUMBER *q);
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extern NUMBER *qbitvalue(long i);
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extern NUMBER *qtenpow(long i);
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/*
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* Transcendental functions. These all take an epsilon argument to
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* specify the required accuracy of the calculation.
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*/
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extern void qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc);
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extern NUMBER *qsqrt(NUMBER *q, NUMBER *epsilon, long R);
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extern NUMBER *qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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extern NUMBER *qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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extern NUMBER *qcos(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qsin(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qln(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qcsc(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacos(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qasin(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qatan(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qasec(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacsc(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacot(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qatan2(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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extern NUMBER *qhypot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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extern NUMBER *qcosh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qsinh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qtanh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qcoth(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qsech(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qcsch(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacosh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qasinh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qatanh(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qasech(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
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extern NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, BOOL wantneg);
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extern NUMBER *qpi(NUMBER *epsilon);
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extern NUMBER *qcatalan(NUMBER *);
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extern NUMBER *qbern(ZVALUE z);
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extern void qfreebern(void);
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extern NUMBER *qeuler(ZVALUE z);
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extern void qfreeeuler(void);
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/*
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* pseudo-seed generator
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*/
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extern NUMBER *pseudo_seed(void);
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/*
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* external swap functions
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*/
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extern NUMBER *swap_b8_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
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extern NUMBER *swap_b16_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
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extern NUMBER *swap_HALF_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
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/*
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* macro expansions to speed this thing up
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*/
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#define qiszero(q) (ziszero((q)->num))
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#define qisneg(q) (zisneg((q)->num))
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#define qispos(q) (zispos((q)->num))
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#define qisint(q) (zisunit((q)->den))
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#define qisfrac(q) (!zisunit((q)->den))
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#define qisunit(q) (zisunit((q)->num) && zisunit((q)->den))
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#define qisone(q) (zisone((q)->num) && zisunit((q)->den))
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#define qisnegone(q) (zisnegone((q)->num) && zisunit((q)->den))
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#define qistwo(q) (zistwo((q)->num) && zisunit((q)->den))
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#define qiseven(q) (zisunit((q)->den) && ziseven((q)->num))
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#define qisodd(q) (zisunit((q)->den) && zisodd((q)->num))
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#define qistwopower(q) (zisunit((q)->den) && zistwopower((q)->num))
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#define qhighbit(q) (zhighbit((q)->num))
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#define qlowbit(q) (zlowbit((q)->num))
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#define qdivcount(q1, q2) (zdivcount((q1)->num, (q2)->num))
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#define qlink(q) ((q)->links++, (q))
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#define qfree(q) {if (--((q)->links) <= 0) qfreenum(q);}
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/*
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* Flags for qparse calls
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*/
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#define QPF_SLASH 0x1 /* allow slash for fractional number */
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#define QPF_IMAG 0x2 /* allow trailing 'i' for imaginary number */
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/*
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* constants used often by the arithmetic routines
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*/
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extern NUMBER _qzero_, _qone_, _qnegone_, _qonehalf_, _qneghalf_, _qonesqbase_;
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extern NUMBER _qtwo_, _qthree_, _qfour_, _qten_;
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extern NUMBER * initnumbs[];
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#endif /* !__QMATH_H__ */
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