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1c839dfede
Add new logn(x, n [,eps]) builtin to compute logarithms to base n. Verify that eps arguments (error tolerance arguments that override the default epsilon value) to builtin functions have proper values. Previously the eps argument had little to no value checks for many builtin functions. Document in help files for builtin functions that take eps arguments, the LIMIT range for such eps values.
285 lines
10 KiB
C
285 lines
10 KiB
C
/*
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* qmath - declarations for extended precision rational arithmetic
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*
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* Copyright (C) 1999-2007,2014,2021,2023 David I. Bell and Landon Curt Noll
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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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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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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(INCLUDE_QMATH_H)
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#define INCLUDE_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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/*
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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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E_FUNC NUMBER *qalloc(void);
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E_FUNC NUMBER *qcopy(NUMBER *q);
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E_FUNC NUMBER *uutoq(FULL i1, FULL i2);
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E_FUNC NUMBER *iitoq(long i1, long i2);
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E_FUNC NUMBER *str2q(char *str);
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E_FUNC NUMBER *itoq(long i);
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E_FUNC NUMBER *utoq(FULL i);
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E_FUNC NUMBER *stoq(SFULL i);
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E_FUNC long qtoi(NUMBER *q);
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E_FUNC FULL qtou(NUMBER *q);
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E_FUNC SFULL qtos(NUMBER *q);
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E_FUNC long qparse(char *str, int flags);
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E_FUNC void qfreenum(NUMBER *q);
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E_FUNC void qprintnum(NUMBER *q, int mode, LEN outdigits);
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E_FUNC void qprintff(NUMBER *q, long width, long precision);
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E_FUNC void qprintfe(NUMBER *q, long width, long precision);
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E_FUNC void qprintfr(NUMBER *q, long width, bool force);
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E_FUNC void qprintfd(NUMBER *q, long width);
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E_FUNC void qprintfx(NUMBER *q, long width);
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E_FUNC void qprintfb(NUMBER *q, long width);
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E_FUNC void qprintfo(NUMBER *q, long width);
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E_FUNC void qprintf(char *, ...);
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E_FUNC void shownumbers(void);
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E_FUNC void showredcdata(void);
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E_FUNC void freeredcdata(void);
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E_FUNC void fitprint(NUMBER *, long);
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/*
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* Basic numeric routines.
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*/
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E_FUNC NUMBER *qaddi(NUMBER *q, long i);
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E_FUNC NUMBER *qmuli(NUMBER *q, long i);
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E_FUNC NUMBER *qdivi(NUMBER *q, long i);
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E_FUNC NUMBER *qqadd(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qsub(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qmul(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qqdiv(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qquo(NUMBER *q1, NUMBER *q2, long rnd);
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E_FUNC NUMBER *qmod(NUMBER *q1, NUMBER *q2, long rnd);
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E_FUNC NUMBER *qmin(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qmax(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qand(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qor(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qxor(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qandnot(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qcomp(NUMBER *q);
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E_FUNC NUMBER *qpowermod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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E_FUNC NUMBER *qpowi(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qsquare(NUMBER *q);
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E_FUNC NUMBER *qneg(NUMBER *q);
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E_FUNC NUMBER *qsign(NUMBER *q);
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E_FUNC NUMBER *qint(NUMBER *q);
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E_FUNC NUMBER *qfrac(NUMBER *q);
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E_FUNC NUMBER *qnum(NUMBER *q);
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E_FUNC NUMBER *qden(NUMBER *q);
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E_FUNC NUMBER *qinv(NUMBER *q);
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E_FUNC NUMBER *qqabs(NUMBER *q);
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E_FUNC NUMBER *qinc(NUMBER *q);
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E_FUNC NUMBER *qdec(NUMBER *q);
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E_FUNC NUMBER *qshift(NUMBER *q, long n);
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E_FUNC NUMBER *qtrunc(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qround(NUMBER *q, long places, long rnd);
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E_FUNC NUMBER *qbtrunc(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qbround(NUMBER *q, long places, long rnd);
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E_FUNC NUMBER *qscale(NUMBER *q, long i);
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E_FUNC bool qdivides(NUMBER *q1, NUMBER *q2);
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E_FUNC bool qcmp(NUMBER *q1, NUMBER *q2);
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E_FUNC bool qcmpi(NUMBER *q, long i);
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E_FUNC FLAG qrel(NUMBER *q1, NUMBER *q2);
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E_FUNC FLAG qreli(NUMBER *q, long i);
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E_FUNC 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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E_FUNC NUMBER *qcomb(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qgcd(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qlcm(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qfact(NUMBER *q);
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E_FUNC NUMBER *qpfact(NUMBER *q);
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E_FUNC NUMBER *qminv(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qfacrem(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qperm(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qgcdrem(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qlowfactor(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qfib(NUMBER *q);
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E_FUNC NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R);
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E_FUNC NUMBER *qcfsim(NUMBER *q, long R);
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E_FUNC NUMBER *qisqrt(NUMBER *q);
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E_FUNC NUMBER *qjacobi(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qiroot(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
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E_FUNC NUMBER *qlcmfact(NUMBER *q);
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E_FUNC NUMBER *qredcin(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qredcout(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qredcmul(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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E_FUNC NUMBER *qredcsquare(NUMBER *q1, NUMBER *q2);
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E_FUNC NUMBER *qredcpower(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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E_FUNC bool qprimetest(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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E_FUNC bool qissquare(NUMBER *q);
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E_FUNC long qilog2(NUMBER *q);
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E_FUNC long qilog10(NUMBER *q);
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E_FUNC NUMBER *qilog(NUMBER *q, ZVALUE base);
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E_FUNC bool qcmpmod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
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E_FUNC bool qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod,
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long rnd);
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E_FUNC FLAG qnear(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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E_FUNC NUMBER *qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base);
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E_FUNC long qprecision(NUMBER *q);
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E_FUNC long qplaces(NUMBER *q, ZVALUE base);
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E_FUNC long qdecplaces(NUMBER *q);
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E_FUNC long qdigits(NUMBER *q, ZVALUE base);
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E_FUNC bool check_epsilon(NUMBER *q);
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E_FUNC void verify_epsilon(NUMBER *q);
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E_FUNC void setepsilon(NUMBER *q);
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E_FUNC NUMBER *qbitvalue(long i);
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E_FUNC NUMBER *qtenpow(long i);
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E_FUNC bool qispowerof2(NUMBER *q, NUMBER **qlog2);
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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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E_FUNC void qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc);
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E_FUNC NUMBER *qsqrt(NUMBER *q, NUMBER *epsilon, long R);
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E_FUNC NUMBER *qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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E_FUNC NUMBER *qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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E_FUNC NUMBER *qcos(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qsin(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qln(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qlog2(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qlogn(NUMBER *q, NUMBER *n, NUMBER *epsilon);
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E_FUNC NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qcsc(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacos(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qasin(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qatan(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qasec(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacsc(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacot(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qatan2(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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E_FUNC NUMBER *qhypot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
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E_FUNC NUMBER *qcosh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qsinh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qtanh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qcoth(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qsech(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qcsch(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacosh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qasinh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qatanh(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qasech(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
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E_FUNC NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, bool wantneg);
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E_FUNC NUMBER *qpi(NUMBER *epsilon);
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E_FUNC NUMBER *qpidiv180(NUMBER *epsilon);
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E_FUNC NUMBER *qpidiv200(NUMBER *epsilon);
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E_FUNC NUMBER *qcatalan(NUMBER *);
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E_FUNC NUMBER *qbern(ZVALUE z);
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E_FUNC void qfreebern(void);
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E_FUNC NUMBER *qeuler(ZVALUE z);
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E_FUNC void qfreeeuler(void);
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/*
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* pseudo-seed generator
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*/
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E_FUNC NUMBER *pseudo_seed(void);
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/*
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* external swap functions
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*/
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E_FUNC NUMBER *swap_b8_in_NUMBER(NUMBER *dest, NUMBER *src, bool all);
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E_FUNC NUMBER *swap_b16_in_NUMBER(NUMBER *dest, NUMBER *src, bool all);
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E_FUNC 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 qistiny(q) (zistiny((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 qisreciprocal(q) (zisunit((q)->num) && !ziszero((q)->den))
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/* operation on #q may be undefined, so replace with an inline-function */
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/* was: #define qlink(q) ((q)->links++, (q)) */
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static inline NUMBER* qlink(NUMBER* q) { if(q) { (q)->links++; } return 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_, _qten_;
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EXTERN NUMBER * initnumbs[];
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#endif /* !INCLUDE_QMATH_H */
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