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calc/qmath.h
Landon Curt Noll db77e29a23 convert ASCII TABs to ASCII SPACEs 
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/*
* qmath - declarations for extended precision rational arithmetic
*
* Copyright (C) 1999-2007,2014,2021,2023 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 19:42:47
* File existed as early as: 1993
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
#if !defined(INCLUDE_QMATH_H)
#define INCLUDE_QMATH_H
#if defined(CALC_SRC) /* if we are building from the calc source tree */
# include "zmath.h"
#else
# include <calc/zmath.h>
#endif
/*
* 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.
*/
E_FUNC NUMBER *qalloc(void);
E_FUNC NUMBER *qcopy(NUMBER *q);
E_FUNC NUMBER *uutoq(FULL i1, FULL i2);
E_FUNC NUMBER *iitoq(long i1, long i2);
E_FUNC NUMBER *str2q(char *str);
E_FUNC NUMBER *itoq(long i);
E_FUNC NUMBER *utoq(FULL i);
E_FUNC NUMBER *stoq(SFULL i);
E_FUNC long qtoi(NUMBER *q);
E_FUNC FULL qtou(NUMBER *q);
E_FUNC SFULL qtos(NUMBER *q);
E_FUNC long qparse(char *str, int flags);
E_FUNC void qfreenum(NUMBER *q);
E_FUNC void qprintnum(NUMBER *q, int mode, LEN outdigits);
E_FUNC void qprintff(NUMBER *q, long width, long precision);
E_FUNC void qprintfe(NUMBER *q, long width, long precision);
E_FUNC void qprintfr(NUMBER *q, long width, bool force);
E_FUNC void qprintfd(NUMBER *q, long width);
E_FUNC void qprintfx(NUMBER *q, long width);
E_FUNC void qprintfb(NUMBER *q, long width);
E_FUNC void qprintfo(NUMBER *q, long width);
E_FUNC void qprintf(char *, ...);
E_FUNC void shownumbers(void);
E_FUNC void showredcdata(void);
E_FUNC void freeredcdata(void);
E_FUNC void fitprint(NUMBER *, long);
/*
* Basic numeric routines.
*/
E_FUNC NUMBER *qaddi(NUMBER *q, long i);
E_FUNC NUMBER *qmuli(NUMBER *q, long i);
E_FUNC NUMBER *qdivi(NUMBER *q, long i);
E_FUNC NUMBER *qqadd(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qsub(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qmul(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qqdiv(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qquo(NUMBER *q1, NUMBER *q2, long rnd);
E_FUNC NUMBER *qmod(NUMBER *q1, NUMBER *q2, long rnd);
E_FUNC NUMBER *qmin(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qmax(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qand(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qor(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qxor(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qandnot(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qcomp(NUMBER *q);
E_FUNC NUMBER *qpowermod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
E_FUNC NUMBER *qpowi(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qsquare(NUMBER *q);
E_FUNC NUMBER *qneg(NUMBER *q);
E_FUNC NUMBER *qsign(NUMBER *q);
E_FUNC NUMBER *qint(NUMBER *q);
E_FUNC NUMBER *qfrac(NUMBER *q);
E_FUNC NUMBER *qnum(NUMBER *q);
E_FUNC NUMBER *qden(NUMBER *q);
E_FUNC NUMBER *qinv(NUMBER *q);
E_FUNC NUMBER *qqabs(NUMBER *q);
E_FUNC NUMBER *qinc(NUMBER *q);
E_FUNC NUMBER *qdec(NUMBER *q);
E_FUNC NUMBER *qshift(NUMBER *q, long n);
E_FUNC NUMBER *qtrunc(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qround(NUMBER *q, long places, long rnd);
E_FUNC NUMBER *qbtrunc(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qbround(NUMBER *q, long places, long rnd);
E_FUNC NUMBER *qscale(NUMBER *q, long i);
E_FUNC bool qdivides(NUMBER *q1, NUMBER *q2);
E_FUNC bool qcmp(NUMBER *q1, NUMBER *q2);
E_FUNC bool qcmpi(NUMBER *q, long i);
E_FUNC FLAG qrel(NUMBER *q1, NUMBER *q2);
E_FUNC FLAG qreli(NUMBER *q, long i);
E_FUNC bool qisset(NUMBER *q, long i);
/*
* More complicated numeric functions.
*/
E_FUNC NUMBER *qcomb(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qgcd(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qlcm(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qfact(NUMBER *q);
E_FUNC NUMBER *qpfact(NUMBER *q);
E_FUNC NUMBER *qminv(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qfacrem(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qperm(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qgcdrem(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qlowfactor(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qfib(NUMBER *q);
E_FUNC NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R);
E_FUNC NUMBER *qcfsim(NUMBER *q, long R);
E_FUNC NUMBER *qisqrt(NUMBER *q);
E_FUNC NUMBER *qjacobi(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qiroot(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
E_FUNC NUMBER *qlcmfact(NUMBER *q);
E_FUNC NUMBER *qredcin(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qredcout(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qredcmul(NUMBER *q1, NUMBER *q2, NUMBER *q3);
E_FUNC NUMBER *qredcsquare(NUMBER *q1, NUMBER *q2);
E_FUNC NUMBER *qredcpower(NUMBER *q1, NUMBER *q2, NUMBER *q3);
E_FUNC bool qprimetest(NUMBER *q1, NUMBER *q2, NUMBER *q3);
E_FUNC bool qissquare(NUMBER *q);
E_FUNC long qilog2(NUMBER *q);
E_FUNC long qilog10(NUMBER *q);
E_FUNC NUMBER *qilog(NUMBER *q, ZVALUE base);
E_FUNC bool qcmpmod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
E_FUNC bool qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod,
long rnd);
E_FUNC FLAG qnear(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC NUMBER *qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base);
E_FUNC long qprecision(NUMBER *q);
E_FUNC long qplaces(NUMBER *q, ZVALUE base);
E_FUNC long qdecplaces(NUMBER *q);
E_FUNC long qdigits(NUMBER *q, ZVALUE base);
E_FUNC bool check_epsilon(NUMBER *q);
E_FUNC void setepsilon(NUMBER *q);
E_FUNC NUMBER *qbitvalue(long i);
E_FUNC NUMBER *qtenpow(long i);
E_FUNC bool qispowerof2(NUMBER *q, NUMBER **qlog2);
/*
* Transcendental functions. These all take an epsilon argument to
* specify the required accuracy of the calculation.
*/
E_FUNC void qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc);
E_FUNC NUMBER *qsqrt(NUMBER *q, NUMBER *epsilon, long R);
E_FUNC NUMBER *qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC NUMBER *qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC NUMBER *qcos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qsin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qln(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qlog2(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qlogn(NUMBER *q, NUMBER *n, NUMBER *epsilon);
E_FUNC NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcsc(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qasin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qatan(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qasec(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacsc(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacot(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qatan2(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC NUMBER *qhypot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
E_FUNC NUMBER *qcosh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qsinh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qtanh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcoth(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qsech(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcsch(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacosh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qasinh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qatanh(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qasech(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, bool wantneg);
E_FUNC NUMBER *qpi(NUMBER *epsilon);
E_FUNC NUMBER *qpidiv180(NUMBER *epsilon);
E_FUNC NUMBER *qpidiv200(NUMBER *epsilon);
E_FUNC NUMBER *qcatalan(NUMBER *);
E_FUNC NUMBER *qbern(ZVALUE z);
E_FUNC void qfreebern(void);
E_FUNC NUMBER *qeuler(ZVALUE z);
E_FUNC void qfreeeuler(void);
/*
* historical trig functions
*/
E_FUNC NUMBER *qversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaversin_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacoversin_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qvercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qavercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcovercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacovercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacovercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qhaversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahaversin_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahaversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qhacoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahacoversin_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahacoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qhavercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahavercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qhacovercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahacovercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qahacovercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qexsec(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaexsec_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaexsec(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qexcsc(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaexcsc_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qaexcsc(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcrd(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacrd_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacrd(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcas(NUMBER *q, NUMBER *epsilon);
/*
* pseudo-seed generator
*/
E_FUNC NUMBER *pseudo_seed(void);
/*
* external swap functions
*/
E_FUNC NUMBER *swap_b8_in_NUMBER(NUMBER *dest, NUMBER *src, bool all);
E_FUNC NUMBER *swap_b16_in_NUMBER(NUMBER *dest, NUMBER *src, bool all);
E_FUNC 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 qistiny(q) (zistiny((q)->num))
#define qhighbit(q) (zhighbit((q)->num))
#define qlowbit(q) (zlowbit((q)->num))
#define qdivcount(q1, q2) (zdivcount((q1)->num, (q2)->num))
#define qisreciprocal(q) (zisunit((q)->num) && !ziszero((q)->den))
/* operation on #q may be undefined, so replace with an inline-function */
/* was: #define qlink(q) ((q)->links++, (q)) */
static inline NUMBER* qlink(NUMBER* q) { if(q) { (q)->links++; } return 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_, _qten_;
EXTERN NUMBER * initnumbs[];
#endif /* !INCLUDE_QMATH_H */
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