qio.c

/*
 * qio - scanf and printf routines for arbitrary precision rational numbers
 *
 * Copyright (C) 1999-2007,2021-2023  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.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * Under source code control:   1993/07/30 19:42:46
 * File existed as early as:    1993
 *
 * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
 */


#include "qmath.h"
#include "config.h"
#include "args.h"

#include "have_unused.h"


#include "errtbl.h"
#include "banned.h"     /* include after system header <> includes */


#define PUTCHAR(ch)             math_chr(ch)
#define PUTSTR(str)             math_str(str)
#define PRINTF1(fmt, a1)        math_fmt(fmt, a1)
#define PRINTF2(fmt, a1, a2)    math_fmt(fmt, a1, a2)

STATIC long     scalefactor;
STATIC ZVALUE   scalenumber = { 0, 0, 0 };


/*
 * Print a formatted string containing arbitrary numbers, similar to printf.
 * ALL numeric arguments to this routine are rational NUMBERs.
 * Various forms of printing such numbers are supplied, in addition
 * to strings and characters.  Output can actually be to any FILE
 * stream or a string.
 */
void
qprintf(char *fmt, ...)
{
        va_list ap;
        NUMBER *q;
        int ch, sign = 1;
        long width = 0, precision = 0;
        int trigger = 0;

        va_start(ap, fmt);
        while ((ch = *fmt++) != '\0') {
                if (trigger == 0) {
                        if (ch == '\\') {
                                ch = *fmt++;
                                switch (ch) {
                                case 'a': ch = '\a'; break;
                                case 'b': ch = '\b'; break;
                                case 'f': ch = '\f'; break;
                                case 'n': ch = '\n'; break;
                                case 'r': ch = '\r'; break;
                                case 't': ch = '\t'; break;
                                case 'v': ch = '\v'; break;
                                case 0:
                                        va_end(ap);
                                        return;
                                }
                                PUTCHAR(ch);
                                continue;
                        }
                        if (ch != '%') {
                                PUTCHAR(ch);
                                continue;
                        }
                        ch = *fmt++;
                        width = 0; precision = 8; sign = 1;
                        trigger = 1;
                }

                switch (ch) {
                case 'd':
                        q = va_arg(ap, NUMBER *);
                        qprintfd(q, width);
                        break;
                case 'f':
                        q = va_arg(ap, NUMBER *);
                        qprintff(q, width, precision);
                        break;
                case 'e':
                        q = va_arg(ap, NUMBER *);
                        qprintfe(q, width, precision);
                        break;
                case 'g':
                        q = va_arg(ap, NUMBER *);
                        /* XXX - we need a qprintfg function */
#if 0   /* XXX - we need a qprintfg() function */
                        qprintfg(q, width, precision);
#else   /* XXX - use qprintfe until we have a qprintfg() function */
                        qprintfe(q, width, precision);
#endif  /* XXX - we need a qprintfg() function */
                        break;
                case 'r':
                case 'R':
                        q = va_arg(ap, NUMBER *);
                        qprintfr(q, width, (bool) (ch == 'R'));
                        break;
                case 'N':
                        q = va_arg(ap, NUMBER *);
                        zprintval(q->num, 0L, width);
                        break;
                case 'D':
                        q = va_arg(ap, NUMBER *);
                        zprintval(q->den, 0L, width);
                        break;
                case 'o':
                        q = va_arg(ap, NUMBER *);
                        qprintfo(q, width);
                        break;
                case 'x':
                        q = va_arg(ap, NUMBER *);
                        qprintfx(q, width);
                        break;
                case 'b':
                        q = va_arg(ap, NUMBER *);
                        qprintfb(q, width);
                        break;
                case 's':
                        PUTSTR(va_arg(ap, char *));
                        break;
                case 'c':
                        PUTCHAR(va_arg(ap, int));
                        break;
                case 0:
                        va_end(ap);
                        return;
                case '-':
                        sign = -1;
                        ch = *fmt++;
                        /*FALLTHRU*/
                default:
                        if (('0' <= ch && ch <= '9') ||
                            ch == '.' || ch == '*') {
                                if (ch == '*') {
                                        q = va_arg(ap, NUMBER *);
                                        width = sign * qtoi(q);
                                        ch = *fmt++;
                                } else if (ch != '.') {
                                        width = ch - '0';
                                        while ('0' <= (ch = *fmt++) &&
                                               ch <= '9')
                                                width = width * 10 + ch - '0';
                                        width *= sign;
                                }
                                if (ch == '.') {
                                        if ((ch = *fmt++) == '*') {
                                                q = va_arg(ap, NUMBER *);
                                                precision = qtoi(q);
                                                ch = *fmt++;
                                        } else {
                                                precision = 0;
                                                while ('0' <= (ch = *fmt++) &&
                                                       ch <= '9')
                                                        precision *= 10+ch-'0';
                                        }
                                }
                        }
                }
        }
        va_end(ap);
}


/*
 * Print a number in the specified output mode.
 * If MODE_DEFAULT is given, then the default output mode is used.
 * Any approximate output is flagged with a leading tilde.
 * Integers are always printed as themselves.
 */
void
qprintnum(NUMBER *q, int outmode, LEN outdigits)
{
        NUMBER tmpval;
        long prec, exp;
        int outmode2 = MODE2_OFF;

        if (outmode == MODE_DEFAULT) {
                outmode = conf->outmode;
                outmode2 = conf->outmode2;
        }
        switch (outmode) {
        case MODE_INT:
                if (conf->tilde_ok && qisfrac(q)) {
                        PUTCHAR('~');
                        if (conf->tilde_space && qisfrac(q)) {
                                PUTCHAR(' ');
                        }
                }
                qprintfd(q, 0L);
                break;

        case MODE_REAL:
                prec = qdecplaces(q);
                if ((prec < 0) || (prec > outdigits)) {
                        if (conf->tilde_ok) {
                            PUTCHAR('~');
                            if (conf->tilde_space) {
                                PUTCHAR(' ');
                            }
                        }
                }
                if (conf->fullzero || (prec < 0) ||
                    (prec > outdigits))
                        prec = outdigits;
                qprintff(q, 0L, prec);
                break;

        case MODE_FRAC:
                qprintfr(q, 0L, false);
                break;

        case MODE_EXP:
                if (qiszero(q)) {
                        PUTCHAR('0');
                        return;
                }
                tmpval = *q;
                tmpval.num.sign = 0;
                exp = qilog10(&tmpval);
                if (exp == 0) {         /* in range to output as real */
                        qprintnum(q, MODE_REAL, outdigits);
                        return;
                }
                tmpval.num = _one_;
                tmpval.den = _one_;
                if (exp > 0)
                        ztenpow(exp, &tmpval.den);
                else
                        ztenpow(-exp, &tmpval.num);
                q = qmul(q, &tmpval);
                zfree(tmpval.num);
                zfree(tmpval.den);
                qprintnum(q, MODE_REAL, outdigits);
                qfree(q);
                PRINTF1("e%ld", exp);
                break;

    case MODE_ENG:
                if (qiszero(q)) {
                        PUTCHAR('0');
                        return;
                }
                tmpval = *q;
                tmpval.num.sign = 0;
                exp = qilog10(&tmpval);
                if (exp == 0) {         /* in range to output as real */
                        qprintnum(q, MODE_REAL, outdigits);
                        return;
                }
                tmpval.num = _one_;
                tmpval.den = _one_;
                if (exp > 0) {
            exp -= exp % 3;
                        ztenpow(exp, &tmpval.den);
        } else {
            long remainder = exp % 3;
            if (remainder)
                exp -= remainder + 3;
                        ztenpow(-exp, &tmpval.num);
        }
                q = qmul(q, &tmpval);
                zfree(tmpval.num);
                zfree(tmpval.den);
                qprintnum(q, MODE_REAL, outdigits);
                qfree(q);
                if (exp) PRINTF1("e%ld", exp);
        break;

        case MODE_REAL_AUTO:
        {
                const int P = conf->outdigits ? conf->outdigits : 1;
                tmpval = *q;
                tmpval.num.sign = 0;
                exp = qilog10(&tmpval);
                if (P > exp && exp >= -P) {
                        qprintnum(q, MODE_REAL, P - 1 - exp);
                } else {
                        qprintnum(q, MODE_EXP, P - 1);
                }
                break;
        }

        case MODE_HEX:
                qprintfx(q, 0L);
                break;

        case MODE_OCTAL:
                qprintfo(q, 0L);
                break;

        case MODE_BINARY:
                qprintfb(q, 0L);
                break;

        default:
                math_error("Bad mode for print");
                not_reached();
        }

        if (outmode2 != MODE2_OFF) {
                PUTSTR(" /* ");
                qprintnum(q, outmode2, outdigits);
                PUTSTR(" */");
        }
}


/*
 * Print a number in floating point representation.
 * Example:  193.784
 */
void
qprintff(NUMBER *q, long width, long precision)
{
        ZVALUE z, z1;

        if (precision != scalefactor) {
                if (scalenumber.v)
                        zfree(scalenumber);
                ztenpow(precision, &scalenumber);
                scalefactor = precision;
        }
        if (scalenumber.v)
                zmul(q->num, scalenumber, &z);
        else
                z = q->num;
        if (qisfrac(q)) {
                zquo(z, q->den, &z1, conf->outround);
                if (z.v != q->num.v)
                        zfree(z);
                z = z1;
        }
        if (qisneg(q) && ziszero(z))
                PUTCHAR('-');
        zprintval(z, precision, width);
        if (z.v != q->num.v)
                zfree(z);
}


/*
 * Print a number in exponential notation.
 * Example: 4.1856e34
 */
/*ARGSUSED*/
void
qprintfe(NUMBER *q, long UNUSED(width), long precision)
{
        long exponent;
        NUMBER q2;
        ZVALUE num, zden, tenpow, tmp;

        if (qiszero(q)) {
                PUTSTR("0.0");
                return;
        }
        num = q->num;
        zden = q->den;
        num.sign = 0;
        exponent = zdigits(num) - zdigits(zden);
        if (exponent > 0) {
                ztenpow(exponent, &tenpow);
                zmul(zden, tenpow, &tmp);
                zfree(tenpow);
                zden = tmp;
        }
        if (exponent < 0) {
                ztenpow(-exponent, &tenpow);
                zmul(num, tenpow, &tmp);
                zfree(tenpow);
                num = tmp;
        }
        if (zrel(num, zden) < 0) {
                zmuli(num, 10L, &tmp);
                if (num.v != q->num.v)
                        zfree(num);
                num = tmp;
                exponent--;
        }
        q2.num = num;
        q2.den = zden;
        q2.num.sign = q->num.sign;
        qprintff(&q2, 0L, precision);
        if (exponent)
                PRINTF1("e%ld", exponent);
        if (num.v != q->num.v)
                zfree(num);
        if (zden.v != q->den.v)
                zfree(zden);
}


/*
 * Print a number in rational representation.
 * Example: 397/37
 */
void
qprintfr(NUMBER *q, long width, bool force)
{
        zprintval(q->num, 0L, width);
        if (force || qisfrac(q)) {
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                PUTCHAR('/');
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                zprintval(q->den, 0L, width);
        }
}


/*
 * Print a number as an integer (truncating fractional part).
 * Example: 958421
 */
void
qprintfd(NUMBER *q, long width)
{
        ZVALUE z;

        if (qisfrac(q)) {
                zquo(q->num, q->den, &z, conf->outround);
                zprintval(z, 0L, width);
                zfree(z);
        } else {
                zprintval(q->num, 0L, width);
        }
}


/*
 * Print a number in hex.
 * This prints the numerator and denominator in hex.
 */
void
qprintfx(NUMBER *q, long width)
{
        zprintx(q->num, width);
        if (qisfrac(q)) {
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                PUTCHAR('/');
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                zprintx(q->den, 0L);
        }
}


/*
 * Print a number in binary.
 * This prints the numerator and denominator in binary.
 */
void
qprintfb(NUMBER *q, long width)
{
        zprintb(q->num, width);
        if (qisfrac(q)) {
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                PUTCHAR('/');
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                zprintb(q->den, 0L);
        }
}


/*
 * Print a number in octal.
 * This prints the numerator and denominator in octal.
 */
void
qprintfo(NUMBER *q, long width)
{
        zprinto(q->num, width);
        if (qisfrac(q)) {
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                PUTCHAR('/');
                if (conf->fraction_space) {
                    PUTCHAR(' ');
                }
                zprinto(q->den, 0L);
        }
}


/*
 * Convert a string to a number in rational, floating point,
 * exponential notation, hex, or octal.
 *      q = str2q(string);
 */
NUMBER *
str2q(char *s)
{
        register NUMBER *q;
        register char *t;
        ZVALUE div, newnum, newden, tmp;
        long decimals, exp;
        bool hex, negexp;

        q = qalloc();
        decimals = 0;
        exp = 0;
        negexp = false;
        hex = false;
        t = s;
        if ((*t == '+') || (*t == '-'))
                t++;
        if ((*t == '0') && ((t[1] == 'x') || (t[1] == 'X'))) {
                hex = true;
                t += 2;
        }
        while (((*t >= '0') && (*t <= '9')) || (hex &&
                (((*t >= 'a') && (*t <= 'f')) || ((*t >= 'A') && (*t <= 'F')))))
                        t++;
        if (*t == '/') {
                t++;
                str2z(t, &q->den);
        } else if ((*t == '.') || (*t == 'e') || (*t == 'E')) {
                if (*t == '.') {
                        t++;
                        while ((*t >= '0') && (*t <= '9')) {
                                t++;
                                decimals++;
                        }
                }
                /*
                 * Parse exponent if any
                 */
                if ((*t == 'e') || (*t == 'E')) {
                        t++;
                        if (*t == '+')
                                t++;
                        else if (*t == '-') {
                                negexp = true;
                                t++;
                        }
                        while ((*t >= '0') && (*t <= '9')) {
                                exp = (exp * 10) + *t++ - '0';
                                if (exp > (MAXLONG/10L)) {
                                        math_error("Exponent too large");
                                        not_reached();
                                }
                        }
                }
                ztenpow(decimals, &q->den);
        }
        str2z(s, &q->num);
        if (qiszero(q)) {
                qfree(q);
                return qlink(&_qzero_);
        }
        /*
         * Apply the exponential if any
         */
        if (exp) {
                ztenpow(exp, &tmp);
                if (negexp) {
                        zmul(q->den, tmp, &newden);
                        zfree(q->den);
                        q->den = newden;
                } else {
                        zmul(q->num, tmp, &newnum);
                        zfree(q->num);
                        q->num = newnum;
                }
                zfree(tmp);
        }
        /*
         * Reduce the fraction to lowest terms
         */
        if (!zisunit(q->num) && !zisunit(q->den)) {
                zgcd(q->num, q->den, &div);
                if (!zisunit(div)) {
                        zequo(q->num, div, &newnum);
                        zfree(q->num);
                        zequo(q->den, div, &newden);
                        zfree(q->den);
                        q->num = newnum;
                        q->den = newden;
                }
                zfree(div);
        }
        return q;
}


/*
 * Parse a number in any of the various legal forms, and return the count
 * of characters that are part of a legal number.  Numbers can be either a
 * decimal integer, possibly two decimal integers separated with a slash, a
 * floating point or exponential number, a hex number beginning with "0x",
 * a binary number beginning with "0b", or an octal number beginning with "0".
 * The flags argument modifies the end of number testing for ease in handling
 * fractions or complex numbers.  Minus one is returned if the number format
 * is definitely illegal.
 */
long
qparse(char *cp, int flags)
{
        char *oldcp;

        oldcp = cp;
        if ((*cp == '+') || (*cp == '-'))
                cp++;
        if ((*cp == '+') || (*cp == '-'))
                return -1;

        /* hex */
        if ((*cp == '0') && ((cp[1] == 'x') || (cp[1] == 'X'))) {
                cp += 2;
                while (((*cp >= '0') && (*cp <= '9')) ||
                        ((*cp >= 'a') && (*cp <= 'f')) ||
                        ((*cp >= 'A') && (*cp <= 'F')))
                                cp++;
                if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
                        cp++;
                if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
                        ((*cp >= '0') && (*cp <= '9')) ||
                        ((*cp >= 'a') && (*cp <= 'z')) ||
                        ((*cp >= 'A') && (*cp <= 'Z')))
                                return -1;
                return (cp - oldcp);
        }

        /* binary */
        if ((*cp == '0') && ((cp[1] == 'b') || (cp[1] == 'B'))) {
                cp += 2;
                while ((*cp == '0') || (*cp == '1'))
                        cp++;
                if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
                        cp++;
                if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
                        ((*cp >= '0') && (*cp <= '9')) ||
                        ((*cp >= 'a') && (*cp <= 'z')) ||
                        ((*cp >= 'A') && (*cp <= 'Z')))
                                return -1;
                return (cp - oldcp);
        }

        /* octal */
        if ((*cp == '0') && (cp[1] >= '0') && (cp[1] <= '9')) {
                while ((*cp >= '0') && (*cp <= '7'))
                        cp++;
                if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
                        cp++;
                if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
                        ((*cp >= '0') && (*cp <= '9')) ||
                        ((*cp >= 'a') && (*cp <= 'z')) ||
                        ((*cp >= 'A') && (*cp <= 'Z')))
                                return -1;
                return (cp - oldcp);
        }

        /*
         * Number is decimal but can still be a fraction or real or exponential
         */
        while ((*cp >= '0') && (*cp <= '9'))
                cp++;
        if (*cp == '/' && flags & QPF_SLASH) {  /* fraction */
                cp++;
                while ((*cp >= '0') && (*cp <= '9'))
                        cp++;
                if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
                        cp++;
                if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
                        ((*cp >= '0') && (*cp <= '9')) ||
                        ((*cp >= 'a') && (*cp <= 'z')) ||
                        ((*cp >= 'A') && (*cp <= 'Z')))
                                return -1;
                return (cp - oldcp);
        }
        if (*cp == '.') {       /* floating point */
                cp++;
                while ((*cp >= '0') && (*cp <= '9'))
                        cp++;
        }
        if ((*cp == 'e') || (*cp == 'E')) {     /* exponential */
                cp++;
                if ((*cp == '+') || (*cp == '-'))
                        cp++;
                if ((*cp == '+') || (*cp == '-'))
                        return -1;
                while ((*cp >= '0') && (*cp <= '9'))
                        cp++;
        }

        if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
                cp++;
        if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
                ((*cp >= '0') && (*cp <= '9')) ||
                ((*cp >= 'a') && (*cp <= 'z')) ||
                ((*cp >= 'A') && (*cp <= 'Z')))
                        return -1;
        return (cp - oldcp);
}


/*
 * Print an integer which is guaranteed to fit in the specified number
 * of columns, using embedded '...' characters if numerator and/or
 * denominator is too large.
 */
void
fitprint(NUMBER *q, long width)
{
        long numdigits, dendigits, digits;
        long width1, width2;
        long n, k;

        if (width < 8)
                width = 8;
        numdigits = zdigits(q->num);
        n = numdigits;
        k = 0;
        while (++k, n)
                n /= 10;
        if (qisint(q)) {
                width -= k;
                k = 16 - k;
                if (k < 2)
                        k = 2;
                PRINTF1("(%ld)", numdigits);
                while (k-- > 0)
                        PUTCHAR(' ');
                fitzprint(q->num, numdigits, width);
                return;
        }
        dendigits = zdigits(q->den);
        PRINTF2("(%ld/%ld)", numdigits, dendigits);
        digits = numdigits + dendigits;
        n = dendigits;
        while (++k, n)
                n /= 10;
        width -= k;
        k = 16 - k;
        if (k < 2)
                k = 2;
        while (k-- > 0)
                PUTCHAR(' ');
        if (digits <= width) {
                qprintf("%r", q);
                return;
        }
        width1 = (width * numdigits)/digits;
        if (width1 < 8)
                width1 = 8;
        width2 = width - width1;
        if (width2 < 8) {
                width2 = 8;
                width1 = width - width2;
        }
        fitzprint(q->num, numdigits, width1);
        if (conf->fraction_space) {
            PUTCHAR(' ');
        }
        PUTCHAR('/');
        if (conf->fraction_space) {
            PUTCHAR(' ');
        }
        fitzprint(q->den, dendigits, width2);
}