c_cpp/etc/calc/qmath.h

   1 /*
   2  * qmath - declarations for extended precision rational arithmetic
   3  *
   4  * Copyright (C) 1999-2007  David I. Bell
   5  *
   6  * Calc is open software; you can redistribute it and/or modify it under
   7  * the terms of the version 2.1 of the GNU Lesser General Public License
   8  * as published by the Free Software Foundation.
   9  *
  10  * Calc is distributed in the hope that it will be useful, but WITHOUT
  11  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  12  * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
  13  * Public License for more details.
  14  *
  15  * A copy of version 2.1 of the GNU Lesser General Public License is
  16  * distributed with calc under the filename COPYING-LGPL.  You should have
  17  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  18  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  19  *
  20  * @(#) $Revision: 30.3 $
  21  * @(#) $Id: qmath.h,v 30.3 2013/08/11 08:41:38 chongo Exp $
  22  * @(#) $Source: /usr/local/src/bin/calc/RCS/qmath.h,v $
  23  *
  24  * Under source code control:   1993/07/30 19:42:47
  25  * File existed as early as:    1993
  26  *
  27  * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
  28  */
  29
  30
  31 #if !defined(__QMATH_H__)
  32 #define __QMATH_H__
  33
  34
  35 #if defined(CALC_SRC)   /* if we are building from the calc source tree */
  36 # include "zmath.h"
  37 #else
  38 # include <calc/zmath.h>
  39 #endif
  40
  41
  42 #define INITCONSTCOUNT 9    /* number of initnumbs[] pre-defined constants */
  43
  44 /*
  45  * Rational arithmetic definitions.
  46  */
  47 struct number {
  48         ZVALUE num;             /* numerator (containing sign) */
  49         ZVALUE den;             /* denominator (always positive) */
  50         long links;             /* number of links to this value */
  51         struct number *next;    /* pointer to next number */
  52 };
  53
  54 typedef struct number NUMBER;
  55
  56 EXTERN NUMBER _qlge_;
  57
  58 /*
  59  * Input. output, allocation, and conversion routines.
  60  */
  61 E_FUNC NUMBER *qalloc(void);
  62 E_FUNC NUMBER *qcopy(NUMBER *q);
  63 E_FUNC NUMBER *uutoq(FULL i1, FULL i2);
  64 E_FUNC NUMBER *iitoq(long i1, long i2);
  65 E_FUNC NUMBER *str2q(char *str);
  66 E_FUNC NUMBER *itoq(long i);
  67 E_FUNC NUMBER *utoq(FULL i);
  68 E_FUNC NUMBER *stoq(SFULL i);
  69 E_FUNC long qtoi(NUMBER *q);
  70 E_FUNC FULL qtou(NUMBER *q);
  71 E_FUNC SFULL qtos(NUMBER *q);
  72 E_FUNC long qparse(char *str, int flags);
  73 E_FUNC void qfreenum(NUMBER *q);
  74 E_FUNC void qprintnum(NUMBER *q, int mode);
  75 E_FUNC void qprintff(NUMBER *q, long width, long precision);
  76 E_FUNC void qprintfe(NUMBER *q, long width, long precision);
  77 E_FUNC void qprintfr(NUMBER *q, long width, BOOL force);
  78 E_FUNC void qprintfd(NUMBER *q, long width);
  79 E_FUNC void qprintfx(NUMBER *q, long width);
  80 E_FUNC void qprintfb(NUMBER *q, long width);
  81 E_FUNC void qprintfo(NUMBER *q, long width);
  82 E_FUNC void qprintf(char *, ...);
  83 E_FUNC void shownumbers(void);
  84 E_FUNC void showredcdata(void);
  85 E_FUNC void freeredcdata(void);
  86 E_FUNC void fitprint(NUMBER *, long);
  87
  88
  89
  90 /*
  91  * Basic numeric routines.
  92  */
  93 E_FUNC NUMBER *qaddi(NUMBER *q, long i);
  94 E_FUNC NUMBER *qmuli(NUMBER *q, long i);
  95 E_FUNC NUMBER *qdivi(NUMBER *q, long i);
  96 E_FUNC NUMBER *qqadd(NUMBER *q1, NUMBER *q2);
  97 E_FUNC NUMBER *qsub(NUMBER *q1, NUMBER *q2);
  98 E_FUNC NUMBER *qmul(NUMBER *q1, NUMBER *q2);
  99 E_FUNC NUMBER *qqdiv(NUMBER *q1, NUMBER *q2);
 100 E_FUNC NUMBER *qquo(NUMBER *q1, NUMBER *q2, long rnd);
 101 E_FUNC NUMBER *qmod(NUMBER *q1, NUMBER *q2, long rnd);
 102 E_FUNC NUMBER *qmin(NUMBER *q1, NUMBER *q2);
 103 E_FUNC NUMBER *qmax(NUMBER *q1, NUMBER *q2);
 104 E_FUNC NUMBER *qand(NUMBER *q1, NUMBER *q2);
 105 E_FUNC NUMBER *qor(NUMBER *q1, NUMBER *q2);
 106 E_FUNC NUMBER *qxor(NUMBER *q1, NUMBER *q2);
 107 E_FUNC NUMBER *qandnot(NUMBER *q1, NUMBER *q2);
 108 E_FUNC NUMBER *qcomp(NUMBER *q);
 109 E_FUNC NUMBER *qpowermod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
 110 E_FUNC NUMBER *qpowi(NUMBER *q1, NUMBER *q2);
 111 E_FUNC NUMBER *qsquare(NUMBER *q);
 112 E_FUNC NUMBER *qneg(NUMBER *q);
 113 E_FUNC NUMBER *qsign(NUMBER *q);
 114 E_FUNC NUMBER *qint(NUMBER *q);
 115 E_FUNC NUMBER *qfrac(NUMBER *q);
 116 E_FUNC NUMBER *qnum(NUMBER *q);
 117 E_FUNC NUMBER *qden(NUMBER *q);
 118 E_FUNC NUMBER *qinv(NUMBER *q);
 119 E_FUNC NUMBER *qqabs(NUMBER *q);
 120 E_FUNC NUMBER *qinc(NUMBER *q);
 121 E_FUNC NUMBER *qdec(NUMBER *q);
 122 E_FUNC NUMBER *qshift(NUMBER *q, long n);
 123 E_FUNC NUMBER *qtrunc(NUMBER *q1, NUMBER *q2);
 124 E_FUNC NUMBER *qround(NUMBER *q, long places, long rnd);
 125 E_FUNC NUMBER *qbtrunc(NUMBER *q1, NUMBER *q2);
 126 E_FUNC NUMBER *qbround(NUMBER *q, long places, long rnd);
 127 E_FUNC NUMBER *qscale(NUMBER *q, long i);
 128 E_FUNC BOOL qdivides(NUMBER *q1, NUMBER *q2);
 129 E_FUNC BOOL qcmp(NUMBER *q1, NUMBER *q2);
 130 E_FUNC BOOL qcmpi(NUMBER *q, long i);
 131 E_FUNC FLAG qrel(NUMBER *q1, NUMBER *q2);
 132 E_FUNC FLAG qreli(NUMBER *q, long i);
 133 E_FUNC BOOL qisset(NUMBER *q, long i);
 134
 135
 136 /*
 137  * More complicated numeric functions.
 138  */
 139 E_FUNC NUMBER *qcomb(NUMBER *q1, NUMBER *q2);
 140 E_FUNC NUMBER *qgcd(NUMBER *q1, NUMBER *q2);
 141 E_FUNC NUMBER *qlcm(NUMBER *q1, NUMBER *q2);
 142 E_FUNC NUMBER *qfact(NUMBER *q);
 143 E_FUNC NUMBER *qpfact(NUMBER *q);
 144 E_FUNC NUMBER *qminv(NUMBER *q1, NUMBER *q2);
 145 E_FUNC NUMBER *qfacrem(NUMBER *q1, NUMBER *q2);
 146 E_FUNC NUMBER *qperm(NUMBER *q1, NUMBER *q2);
 147 E_FUNC NUMBER *qgcdrem(NUMBER *q1, NUMBER *q2);
 148 E_FUNC NUMBER *qlowfactor(NUMBER *q1, NUMBER *q2);
 149 E_FUNC NUMBER *qfib(NUMBER *q);
 150 E_FUNC NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R);
 151 E_FUNC NUMBER *qcfsim(NUMBER *q, long R);
 152 E_FUNC NUMBER *qisqrt(NUMBER *q);
 153 E_FUNC NUMBER *qjacobi(NUMBER *q1, NUMBER *q2);
 154 E_FUNC NUMBER *qiroot(NUMBER *q1, NUMBER *q2);
 155 E_FUNC NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
 156 E_FUNC NUMBER *qlcmfact(NUMBER *q);
 157 E_FUNC NUMBER *qredcin(NUMBER *q1, NUMBER *q2);
 158 E_FUNC NUMBER *qredcout(NUMBER *q1, NUMBER *q2);
 159 E_FUNC NUMBER *qredcmul(NUMBER *q1, NUMBER *q2, NUMBER *q3);
 160 E_FUNC NUMBER *qredcsquare(NUMBER *q1, NUMBER *q2);
 161 E_FUNC NUMBER *qredcpower(NUMBER *q1, NUMBER *q2, NUMBER *q3);
 162 E_FUNC BOOL qprimetest(NUMBER *q1, NUMBER *q2, NUMBER *q3);
 163 E_FUNC BOOL qissquare(NUMBER *q);
 164 E_FUNC long qilog2(NUMBER *q);
 165 E_FUNC long qilog10(NUMBER *q);
 166 E_FUNC NUMBER *qilog(NUMBER *q, ZVALUE base);
 167 E_FUNC BOOL qcmpmod(NUMBER *q1, NUMBER *q2, NUMBER *q3);
 168 E_FUNC BOOL qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod,
 169                     long rnd);
 170 E_FUNC FLAG qnear(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
 171 E_FUNC NUMBER *qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base);
 172 E_FUNC long qprecision(NUMBER *q);
 173 E_FUNC long qplaces(NUMBER *q, ZVALUE base);
 174 E_FUNC long qdecplaces(NUMBER *q);
 175 E_FUNC long qdigits(NUMBER *q, ZVALUE base);
 176 E_FUNC void setepsilon(NUMBER *q);
 177 E_FUNC NUMBER *qbitvalue(long i);
 178 E_FUNC NUMBER *qtenpow(long i);
 179
 180
 181 /*
 182  * Transcendental functions.  These all take an epsilon argument to
 183  * specify the required accuracy of the calculation.
 184  */
 185 E_FUNC void qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc);
 186 E_FUNC NUMBER *qsqrt(NUMBER *q, NUMBER *epsilon, long R);
 187 E_FUNC NUMBER *qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
 188 E_FUNC NUMBER *qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
 189 E_FUNC NUMBER *qcos(NUMBER *q, NUMBER *epsilon);
 190 E_FUNC NUMBER *qsin(NUMBER *q, NUMBER *epsilon);
 191 E_FUNC NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
 192 E_FUNC NUMBER *qln(NUMBER *q, NUMBER *epsilon);
 193 E_FUNC NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
 194 E_FUNC NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
 195 E_FUNC NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
 196 E_FUNC NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
 197 E_FUNC NUMBER *qcsc(NUMBER *q, NUMBER *epsilon);
 198 E_FUNC NUMBER *qacos(NUMBER *q, NUMBER *epsilon);
 199 E_FUNC NUMBER *qasin(NUMBER *q, NUMBER *epsilon);
 200 E_FUNC NUMBER *qatan(NUMBER *q, NUMBER *epsilon);
 201 E_FUNC NUMBER *qasec(NUMBER *q, NUMBER *epsilon);
 202 E_FUNC NUMBER *qacsc(NUMBER *q, NUMBER *epsilon);
 203 E_FUNC NUMBER *qacot(NUMBER *q, NUMBER *epsilon);
 204 E_FUNC NUMBER *qatan2(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
 205 E_FUNC NUMBER *qhypot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon);
 206 E_FUNC NUMBER *qcosh(NUMBER *q, NUMBER *epsilon);
 207 E_FUNC NUMBER *qsinh(NUMBER *q, NUMBER *epsilon);
 208 E_FUNC NUMBER *qtanh(NUMBER *q, NUMBER *epsilon);
 209 E_FUNC NUMBER *qcoth(NUMBER *q, NUMBER *epsilon);
 210 E_FUNC NUMBER *qsech(NUMBER *q, NUMBER *epsilon);
 211 E_FUNC NUMBER *qcsch(NUMBER *q, NUMBER *epsilon);
 212 E_FUNC NUMBER *qacosh(NUMBER *q, NUMBER *epsilon);
 213 E_FUNC NUMBER *qasinh(NUMBER *q, NUMBER *epsilon);
 214 E_FUNC NUMBER *qatanh(NUMBER *q, NUMBER *epsilon);
 215 E_FUNC NUMBER *qasech(NUMBER *q, NUMBER *epsilon);
 216 E_FUNC NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
 217 E_FUNC NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
 218 E_FUNC NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, BOOL wantneg);
 219 E_FUNC NUMBER *qpi(NUMBER *epsilon);
 220 E_FUNC NUMBER *qcatalan(NUMBER *);
 221 E_FUNC NUMBER *qbern(ZVALUE z);
 222 E_FUNC void qfreebern(void);
 223 E_FUNC NUMBER *qeuler(ZVALUE z);
 224 E_FUNC void qfreeeuler(void);
 225
 226
 227 /*
 228  * pseudo-seed generator
 229  */
 230 E_FUNC NUMBER *pseudo_seed(void);
 231
 232
 233 /*
 234  * external swap functions
 235  */
 236 E_FUNC NUMBER *swap_b8_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
 237 E_FUNC NUMBER *swap_b16_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
 238 E_FUNC NUMBER *swap_HALF_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
 239
 240
 241 /*
 242  * macro expansions to speed this thing up
 243  */
 244 #define qiszero(q)      (ziszero((q)->num))
 245 #define qisneg(q)       (zisneg((q)->num))
 246 #define qispos(q)       (zispos((q)->num))
 247 #define qisint(q)       (zisunit((q)->den))
 248 #define qisfrac(q)      (!zisunit((q)->den))
 249 #define qisunit(q)      (zisunit((q)->num) && zisunit((q)->den))
 250 #define qisone(q)       (zisone((q)->num) && zisunit((q)->den))
 251 #define qisnegone(q)    (zisnegone((q)->num) && zisunit((q)->den))
 252 #define qistwo(q)       (zistwo((q)->num) && zisunit((q)->den))
 253 #define qiseven(q)      (zisunit((q)->den) && ziseven((q)->num))
 254 #define qisodd(q)       (zisunit((q)->den) && zisodd((q)->num))
 255 #define qistwopower(q)  (zisunit((q)->den) && zistwopower((q)->num))
 256 #define qistiny(q)      (zistiny((q)->num))
 257
 258 #define qhighbit(q)     (zhighbit((q)->num))
 259 #define qlowbit(q)      (zlowbit((q)->num))
 260 #define qdivcount(q1, q2)       (zdivcount((q1)->num, (q2)->num))
 261 #define qlink(q)        ((q)->links++, (q))
 262
 263 #define qfree(q)        {if (--((q)->links) <= 0) qfreenum(q);}
 264
 265
 266 /*
 267  * Flags for qparse calls
 268  */
 269 #define QPF_SLASH       0x1     /* allow slash for fractional number */
 270 #define QPF_IMAG        0x2     /* allow trailing 'i' for imaginary number */
 271
 272
 273 /*
 274  * constants used often by the arithmetic routines
 275  */
 276 EXTERN NUMBER _qzero_, _qone_, _qnegone_, _qonehalf_, _qneghalf_, _qonesqbase_;
 277 EXTERN NUMBER _qtwo_, _qthree_, _qfour_, _qten_;
 278 EXTERN NUMBER * initnumbs[];
 279
 280
 281 #endif /* !__QMATH_H__ */