/*
 * qmath - extended precision rational arithmetic primitive routines
 *
 * Copyright (C) 1999-2007,2014,2021-2023  David I. Bell, Landon Curt Noll and Ernest Bowen
 *
 * Primary author:  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:   1990/02/15 01:48:21
 * File existed as early as:    before 1990
 *
 * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
 */


#include <stdio.h>
#include "qmath.h"
#include "config.h"


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


NUMBER _qzero_ =        { { _zeroval_, 1, 0 }, { _oneval_, 1, 0 }, 1, NULL };
NUMBER _qone_ =         { { _oneval_, 1, 0  }, { _oneval_, 1, 0 }, 1, NULL };
NUMBER _qtwo_ =         { { _twoval_, 1, 0 }, { _oneval_, 1, 0 }, 1, NULL };
NUMBER _qten_ =         { { _tenval_, 1, 0 }, { _oneval_, 1, 0 }, 1, NULL };
NUMBER _qnegone_ =      { { _oneval_, 1, 1 }, { _oneval_, 1, 0 }, 1, NULL };
NUMBER _qonehalf_ =     { { _oneval_, 1, 0 }, { _twoval_, 1, 0 }, 1, NULL };
NUMBER _qneghalf_ =     { { _oneval_, 1, 1 }, { _twoval_, 1, 0 }, 1, NULL };
NUMBER _qonesqbase_ =   { { _oneval_, 1, 0 }, { _sqbaseval_, 2, 0 }, 1, NULL };

NUMBER * initnumbs[] = {&_qzero_, &_qone_, &_qtwo_,
        &_qten_, &_qnegone_, &_qonehalf_, &_qneghalf_,
        &_qonesqbase_,
        NULL    /* must be last */
};


/*
 * Create another copy of a number.
 *      q2 = qcopy(q1);
 */
NUMBER *
qcopy(NUMBER *q)
{
        register NUMBER *r;

        r = qalloc();
        r->num.sign = q->num.sign;
        if (!zisunit(q->num)) {
                r->num.len = q->num.len;
                r->num.v = alloc(r->num.len);
                zcopyval(q->num, r->num);
        }
        if (!zisunit(q->den)) {
                r->den.len = q->den.len;
                r->den.v = alloc(r->den.len);
                zcopyval(q->den, r->den);
        }
        return r;
}


/*
 * Convert a number to a normal integer.
 *      i = qtoi(q);
 */
long
qtoi(NUMBER *q)
{
        long i;
        ZVALUE res;

        if (qisint(q))
                return ztoi(q->num);
        zquo(q->num, q->den, &res, 0);
        i = ztoi(res);
        zfree(res);
        return i;
}


/*
 * Convert a normal integer into a number.
 *      q = itoq(i);
 */
NUMBER *
itoq(long i)
{
        register NUMBER *q;

        if ((i >= -1) && (i <= 10)) {
                switch ((int) i) {
                case 0: q = &_qzero_; break;
                case 1: q = &_qone_; break;
                case 2: q = &_qtwo_; break;
                case 10: q = &_qten_; break;
                case -1: q = &_qnegone_; break;
                default: q = NULL;
                }
                if (q)
                        return qlink(q);
        }
        q = qalloc();
        itoz(i, &q->num);
        return q;
}


/*
 * Convert a number to a normal unsigned integer.
 *      u = qtou(q);
 */
FULL
qtou(NUMBER *q)
{
        FULL i;
        ZVALUE res;

        if (qisint(q))
                return ztou(q->num);
        zquo(q->num, q->den, &res, 0);
        i = ztou(res);
        zfree(res);
        return i;
}


/*
 * Convert a number to a normal signed integer.
 *      s = qtos(q);
 */
SFULL
qtos(NUMBER *q)
{
        SFULL i;
        ZVALUE res;

        if (qisint(q))
                return ztos(q->num);
        zquo(q->num, q->den, &res, 0);
        i = ztos(res);
        zfree(res);
        return i;
}


/*
 * Convert a normal unsigned integer into a number.
 *      q = utoq(i);
 */
NUMBER *
utoq(FULL i)
{
        register NUMBER *q;

        if (i <= 10) {
                switch ((int) i) {
                case 0: q = &_qzero_; break;
                case 1: q = &_qone_; break;
                case 2: q = &_qtwo_; break;
                case 10: q = &_qten_; break;
                default: q = NULL;
                }
                if (q)
                        return qlink(q);
        }
        q = qalloc();
        utoz(i, &q->num);
        return q;
}


/*
 * Convert a normal signed integer into a number.
 *      q = stoq(s);
 */
NUMBER *
stoq(SFULL i)
{
        register NUMBER *q;

        if (i <= 10) {
                switch ((int) i) {
                case 0: q = &_qzero_; break;
                case 1: q = &_qone_; break;
                case 2: q = &_qtwo_; break;
                case 10: q = &_qten_; break;
                default: q = NULL;
                }
                if (q)
                        return qlink(q);
        }
        q = qalloc();
        stoz(i, &q->num);
        return q;
}


/*
 * Create a number from the given FULL numerator and denominator.
 *      q = uutoq(inum, iden);
 */
NUMBER *
uutoq(FULL inum, FULL iden)
{
        register NUMBER *q;
        FULL d;
        bool sign;

        if (iden == 0) {
                math_error("Division by zero");
                not_reached();
        }
        if (inum == 0)
                return qlink(&_qzero_);
        sign = 0;
        d = uugcd(inum, iden);
        inum /= d;
        iden /= d;
        if (iden == 1)
                return utoq(inum);
        q = qalloc();
        if (inum != 1)
                utoz(inum, &q->num);
        utoz(iden, &q->den);
        q->num.sign = sign;
        return q;
}


/*
 * Create a number from the given integral numerator and denominator.
 *      q = iitoq(inum, iden);
 */
NUMBER *
iitoq(long inum, long iden)
{
        register NUMBER *q;
        long d;
        bool sign;

        if (iden == 0) {
                math_error("Division by zero");
                not_reached();
        }
        if (inum == 0)
                return qlink(&_qzero_);
        sign = 0;
        if (inum < 0) {
                sign = 1;
                inum = -inum;
        }
        if (iden < 0) {
                sign = 1 - sign;
                iden = -iden;
        }
        d = iigcd(inum, iden);
        inum /= d;
        iden /= d;
        if (iden == 1)
                return itoq(sign ? -inum : inum);
        q = qalloc();
        if (inum != 1)
                itoz(inum, &q->num);
        itoz(iden, &q->den);
        q->num.sign = sign;
        return q;
}


/*
 * Add two numbers to each other.
 *      q3 = qqadd(q1, q2);
 */
NUMBER *
qqadd(NUMBER *q1, NUMBER *q2)
{
        NUMBER *r;
        ZVALUE t1, t2, temp, d1, d2, vpd1, upd1;

        if (qiszero(q1))
                return qlink(q2);
        if (qiszero(q2))
                return qlink(q1);
        r = qalloc();
        /*
         * If either number is an integer, then the result is easy.
         */
        if (qisint(q1) && qisint(q2)) {
                zadd(q1->num, q2->num, &r->num);
                return r;
        }
        if (qisint(q2)) {
                zmul(q1->den, q2->num, &temp);
                zadd(q1->num, temp, &r->num);
                zfree(temp);
                zcopy(q1->den, &r->den);
                return r;
        }
        if (qisint(q1)) {
                zmul(q2->den, q1->num, &temp);
                zadd(q2->num, temp, &r->num);
                zfree(temp);
                zcopy(q2->den, &r->den);
                return r;
        }
        /*
         * Both arguments are true fractions, so we need more work.
         * If the denominators are relatively prime, then the answer is the
         * straightforward cross product result with no need for reduction.
         */
        zgcd(q1->den, q2->den, &d1);
        if (zisunit(d1)) {
                zfree(d1);
                zmul(q1->num, q2->den, &t1);
                zmul(q1->den, q2->num, &t2);
                zadd(t1, t2, &r->num);
                zfree(t1);
                zfree(t2);
                zmul(q1->den, q2->den, &r->den);
                return r;
        }
        /*
         * The calculation is now more complicated.
         * See Knuth Vol 2 for details.
         */
        zquo(q2->den, d1, &vpd1, 0);
        zquo(q1->den, d1, &upd1, 0);
        zmul(q1->num, vpd1, &t1);
        zmul(q2->num, upd1, &t2);
        zadd(t1, t2, &temp);
        zfree(t1);
        zfree(t2);
        zfree(vpd1);
        zgcd(temp, d1, &d2);
        zfree(d1);
        if (zisunit(d2)) {
                zfree(d2);
                r->num = temp;
                zmul(upd1, q2->den, &r->den);
                zfree(upd1);
                return r;
        }
        zquo(temp, d2, &r->num, 0);
        zfree(temp);
        zquo(q2->den, d2, &temp, 0);
        zfree(d2);
        zmul(temp, upd1, &r->den);
        zfree(temp);
        zfree(upd1);
        return r;
}


/*
 * Subtract one number from another.
 *      q3 = qsub(q1, q2);
 */
NUMBER *
qsub(NUMBER *q1, NUMBER *q2)
{
        NUMBER *r;

        if (q1 == q2)
                return qlink(&_qzero_);
        if (qiszero(q2))
                return qlink(q1);
        if (qisint(q1) && qisint(q2)) {
                r = qalloc();
                zsub(q1->num, q2->num, &r->num);
                return r;
        }
        q2 = qneg(q2);
        if (qiszero(q1))
                return q2;
        r = qqadd(q1, q2);
        qfree(q2);
        return r;
}


/*
 * Increment a number by one.
 */
NUMBER *
qinc(NUMBER *q)
{
        NUMBER *r;

        r = qalloc();
        if (qisint(q)) {
                zadd(q->num, _one_, &r->num);
                return r;
        }
        zadd(q->num, q->den, &r->num);
        zcopy(q->den, &r->den);
        return r;
}


/*
 * Decrement a number by one.
 */
NUMBER *
qdec(NUMBER *q)
{
        NUMBER *r;

        r = qalloc();
        if (qisint(q)) {
                zsub(q->num, _one_, &r->num);
                return r;
        }
        zsub(q->num, q->den, &r->num);
        zcopy(q->den, &r->den);
        return r;
}


/*
 * Add a normal small integer value to an arbitrary number.
 */
NUMBER *
qaddi(NUMBER *q1, long n)
{
        NUMBER addnum;          /* temporary number */
        HALF addval[2];         /* value of small number */
        bool neg;               /* true if number is neg */
#if LONG_BITS > BASEB
        FULL nf;
#endif

        if (n == 0)
                return qlink(q1);
        if (n == 1)
                return qinc(q1);
        if (n == -1)
                return qdec(q1);
        if (qiszero(q1))
                return itoq(n);
        addnum.num.sign = 0;
        addnum.num.v = addval;
        addnum.den = _one_;
        neg = (n < 0);
        if (neg)
                n = -n;
        addval[0] = (HALF) n;
#if LONG_BITS > BASEB
        nf = (((FULL) n) >> BASEB);
        if (nf) {
                addval[1] = (HALF) nf;
                addnum.num.len = 2;
        }
#else
        addnum.num.len = 1;
#endif
        if (neg)
                return qsub(q1, &addnum);
        else
                return qqadd(q1, &addnum);
}


/*
 * Multiply two numbers.
 *      q3 = qmul(q1, q2);
 */
NUMBER *
qmul(NUMBER *q1, NUMBER *q2)
{
        NUMBER *r;                      /* returned value */
        ZVALUE n1, n2, d1, d2;          /* numerators and denominators */
        ZVALUE tmp;

        if (qiszero(q1) || qiszero(q2))
                return qlink(&_qzero_);
        if (qisone(q1))
                return qlink(q2);
        if (qisone(q2))
                return qlink(q1);
        if (qisint(q1) && qisint(q2)) { /* easy results if integers */
                r = qalloc();
                zmul(q1->num, q2->num, &r->num);
                return r;
        }
        n1 = q1->num;
        n2 = q2->num;
        d1 = q1->den;
        d2 = q2->den;
        if (ziszero(d1) || ziszero(d2)) {
                math_error("Division by zero");
                not_reached();
        }
        if (ziszero(n1) || ziszero(n2))
                return qlink(&_qzero_);
        if (!zisunit(n1) && !zisunit(d2)) {     /* possibly reduce */
                zgcd(n1, d2, &tmp);
                if (!zisunit(tmp)) {
                        zequo(q1->num, tmp, &n1);
                        zequo(q2->den, tmp, &d2);
                }
                zfree(tmp);
        }
        if (!zisunit(n2) && !zisunit(d1)) {     /* again possibly reduce */
                zgcd(n2, d1, &tmp);
                if (!zisunit(tmp)) {
                        zequo(q2->num, tmp, &n2);
                        zequo(q1->den, tmp, &d1);
                }
                zfree(tmp);
        }
        r = qalloc();
        zmul(n1, n2, &r->num);
        zmul(d1, d2, &r->den);
        if (q1->num.v != n1.v)
                zfree(n1);
        if (q1->den.v != d1.v)
                zfree(d1);
        if (q2->num.v != n2.v)
                zfree(n2);
        if (q2->den.v != d2.v)
                zfree(d2);
        return r;
}


/*
 * Multiply a number by a small integer.
 *      q2 = qmuli(q1, n);
 */
NUMBER *
qmuli(NUMBER *q, long n)
{
        NUMBER *r;
        long d;                 /* gcd of multiplier and denominator */
        int sign;

        if ((n == 0) || qiszero(q))
                return qlink(&_qzero_);
        if (n == 1)
                return qlink(q);
        r = qalloc();
        if (qisint(q)) {
                zmuli(q->num, n, &r->num);
                return r;
        }
        sign = 1;
        if (n < 0) {
                n = -n;
                sign = -1;
        }
        d = zmodi(q->den, n);
        d = iigcd(d, n);
        zmuli(q->num, (n * sign) / d, &r->num);
        (void) zdivi(q->den, d, &r->den);
        return r;
}


/*
 * Divide two numbers (as fractions).
 *      q3 = qqdiv(q1, q2);
 */
NUMBER *
qqdiv(NUMBER *q1, NUMBER *q2)
{
        NUMBER temp;

        if (qiszero(q2)) {
                math_error("Division by zero");
                not_reached();
        }
        if ((q1 == q2) || !qcmp(q1, q2))
                return qlink(&_qone_);
        if (qisone(q1))
                return qinv(q2);
        temp.num = q2->den;
        temp.den = q2->num;
        temp.num.sign = temp.den.sign;
        temp.den.sign = 0;
        temp.links = 1;
        return qmul(q1, &temp);
}


/*
 * Divide a number by a small integer.
 *      q2 = qdivi(q1, n);
 */
NUMBER *
qdivi(NUMBER *q, long n)
{
        NUMBER *r;
        long d;                 /* gcd of divisor and numerator */
        int sign;

        if (n == 0) {
                math_error("Division by zero");
                not_reached();
        }
        if ((n == 1) || qiszero(q))
                return qlink(q);
        sign = 1;
        if (n < 0) {
                n = -n;
                sign = -1;
        }
        r = qalloc();
        d = zmodi(q->num, n);
        d = iigcd(d, n);
        (void) zdivi(q->num, d * sign, &r->num);
        zmuli(q->den, n / d, &r->den);
        return r;
}


/*
 * Return the integer quotient of a pair of numbers
 * If q1/q2 is an integer qquo(q1, q2) returns this integer
 * If q2 is zero, zero is returned
 * In other cases whether rounding is down, up, towards zero, etc.
 * is determined by rnd.
 */
NUMBER *
qquo(NUMBER *q1, NUMBER *q2, long rnd)
{
        ZVALUE tmp, tmp1, tmp2;
        NUMBER *q;

        if (qiszero(q1) || qiszero(q2))
                return qlink(&_qzero_);
        if (qisint(q1) && qisint(q2)) {
                zquo(q1->num, q2->num, &tmp, rnd);
        } else {
                zmul(q1->num, q2->den, &tmp1);
                zmul(q2->num, q1->den, &tmp2);
                zquo(tmp1, tmp2, &tmp, rnd);
                zfree(tmp1);
                zfree(tmp2);
        }
        if (ziszero(tmp)) {
                zfree(tmp);
                return qlink(&_qzero_);
        }
        q = qalloc();
        q->num = tmp;
        return q;
}


/*
 * Return the absolute value of a number.
 *      q2 = qqabs(q1);
 */
NUMBER *
qqabs(NUMBER *q)
{
        register NUMBER *r;

        if (q->num.sign == 0)
                return qlink(q);
        r = qalloc();
        if (!zisunit(q->num))
                zcopy(q->num, &r->num);
        if (!zisunit(q->den))
                zcopy(q->den, &r->den);
        r->num.sign = 0;
        return r;
}


/*
 * Negate a number.
 *      q2 = qneg(q1);
 */
NUMBER *
qneg(NUMBER *q)
{
        register NUMBER *r;

        if (qiszero(q))
                return qlink(&_qzero_);
        r = qalloc();
        if (!zisunit(q->num))
                zcopy(q->num, &r->num);
        if (!zisunit(q->den))
                zcopy(q->den, &r->den);
        r->num.sign = !q->num.sign;
        return r;
}


/*
 * Return the sign of a number (-1, 0 or 1)
 */
NUMBER *
qsign(NUMBER *q)
{
        if (qiszero(q))
                return qlink(&_qzero_);
        if (qisneg(q))
                return qlink(&_qnegone_);
        return qlink(&_qone_);
}


/*
 * Invert a number.
 *      q2 = qinv(q1);
 */
NUMBER *
qinv(NUMBER *q)
{
        register NUMBER *r;

        if (qisunit(q)) {
                r = (qisneg(q) ? &_qnegone_ : &_qone_);
                return qlink(r);
        }
        if (qiszero(q)) {
                math_error("Division by zero");
                not_reached();
        }
        r = qalloc();
        if (!zisunit(q->num))
                zcopy(q->num, &r->den);
        if (!zisunit(q->den))
                zcopy(q->den, &r->num);
        r->num.sign = q->num.sign;
        r->den.sign = 0;
        return r;
}


/*
 * Return just the numerator of a number.
 *      q2 = qnum(q1);
 */
NUMBER *
qnum(NUMBER *q)
{
        register NUMBER *r;

        if (qisint(q))
                return qlink(q);
        if (zisunit(q->num)) {
                r = (qisneg(q) ? &_qnegone_ : &_qone_);
                return qlink(r);
        }
        r = qalloc();
        zcopy(q->num, &r->num);
        return r;
}


/*
 * Return just the denominator of a number.
 *      q2 = qden(q1);
 */
NUMBER *
qden(NUMBER *q)
{
        register NUMBER *r;

        if (qisint(q))
                return qlink(&_qone_);
        r = qalloc();
        zcopy(q->den, &r->num);
        return r;
}


/*
 * Return the fractional part of a number.
 *      q2 = qfrac(q1);
 */
NUMBER *
qfrac(NUMBER *q)
{
        register NUMBER *r;

        if (qisint(q))
                return qlink(&_qzero_);
        if ((q->num.len < q->den.len) || ((q->num.len == q->den.len) &&
                (q->num.v[q->num.len - 1] < q->den.v[q->num.len - 1])))
                        return qlink(q);
        r = qalloc();
        zmod(q->num, q->den, &r->num, 2);
        zcopy(q->den, &r->den);
        return r;
}


/*
 * Return the integral part of a number.
 *      q2 = qint(q1);
 */
NUMBER *
qint(NUMBER *q)
{
        register NUMBER *r;

        if (qisint(q))
                return qlink(q);
        if ((q->num.len < q->den.len) || ((q->num.len == q->den.len) &&
                (q->num.v[q->num.len - 1] < q->den.v[q->num.len - 1])))
                        return qlink(&_qzero_);
        r = qalloc();
        zquo(q->num, q->den, &r->num, 2);
        return r;
}


/*
 * Compute the square of a number.
 */
NUMBER *
qsquare(NUMBER *q)
{
        ZVALUE num, zden;

        if (qiszero(q))
                return qlink(&_qzero_);
        if (qisunit(q))
                return qlink(&_qone_);
        num = q->num;
        zden = q->den;
        q = qalloc();
        if (!zisunit(num))
                zsquare(num, &q->num);
        if (!zisunit(zden))
                zsquare(zden, &q->den);
        return q;
}


/*
 * Shift an integer by a given number of bits. This multiplies the number
 * by the appropriate power of two.  Positive numbers shift left, negative
 * ones shift right.  Low bits are truncated when shifting right.
 */
NUMBER *
qshift(NUMBER *q, long n)
{
        register NUMBER *r;

        if (qisfrac(q)) {
                math_error("Shift of non-integer");
                not_reached();
        }
        if (qiszero(q) || (n == 0))
                return qlink(q);
        if (n <= -(q->num.len * BASEB))
                return qlink(&_qzero_);
        r = qalloc();
        zshift(q->num, n, &r->num);
        return r;
}


/*
 * Scale a number by a power of two, as in:
 *      ans = q * 2^n.
 * This is similar to shifting, except that fractions work.
 */
NUMBER *
qscale(NUMBER *q, long pow)
{
        long numshift, denshift, tmp;
        NUMBER *r;

        if (qiszero(q) || (pow == 0))
                return qlink(q);
        numshift = zisodd(q->num) ? 0 : zlowbit(q->num);
        denshift = zisodd(q->den) ? 0 : zlowbit(q->den);
        if (pow > 0) {
                tmp = pow;
                if (tmp > denshift)
                tmp = denshift;
                denshift = -tmp;
                numshift = (pow - tmp);
        } else {
                pow = -pow;
                tmp = pow;
                if (tmp > numshift)
                        tmp = numshift;
                numshift = -tmp;
                denshift = (pow - tmp);
        }
        r = qalloc();
        if (numshift)
                zshift(q->num, numshift, &r->num);
        else
                zcopy(q->num, &r->num);
        if (denshift)
                zshift(q->den, denshift, &r->den);
        else
                zcopy(q->den, &r->den);
        return r;
}


/*
 * Return the minimum of two numbers.
 */
NUMBER *
qmin(NUMBER *q1, NUMBER *q2)
{
        if (q1 == q2)
                return qlink(q1);
        if (qrel(q1, q2) > 0)
                q1 = q2;
        return qlink(q1);
}


/*
 * Return the maximum of two numbers.
 */
NUMBER *
qmax(NUMBER *q1, NUMBER *q2)
{
        if (q1 == q2)
                return qlink(q1);
        if (qrel(q1, q2) < 0)
                q1 = q2;
        return qlink(q1);
}


/*
 * Perform the bitwise OR of two integers.
 */
NUMBER *
qor(NUMBER *q1, NUMBER *q2)
{
        register NUMBER *r;
        NUMBER *q1tmp, *q2tmp, *q;

        if (qisfrac(q1) || qisfrac(q2)) {
                math_error("Non-integers for bitwise or");
                not_reached();
        }
        if (qcmp(q1,q2) == 0 || qiszero(q2))
                return qlink(q1);
        if (qiszero(q1))
                return qlink(q2);
        if (qisneg(q1)) {
                q1tmp = qcomp(q1);
                if (qisneg(q2)) {
                        q2tmp = qcomp(q2);
                        q = qand(q1tmp,q2tmp);
                        r = qcomp(q);
                        qfree(q1tmp);
                        qfree(q2tmp);
                        qfree(q);
                        return r;
                }
                q = qandnot(q1tmp, q2);
                qfree(q1tmp);
                r = qcomp(q);
                qfree(q);
                return r;
        }
        if (qisneg(q2)) {
                q2tmp = qcomp(q2);
                q = qandnot(q2tmp, q1);
                qfree(q2tmp);
                r = qcomp(q);
                qfree(q);
                return r;
        }
        r = qalloc();
        zor(q1->num, q2->num, &r->num);
        return r;
}


/*
 * Perform the bitwise AND of two integers.
 */
NUMBER *
qand(NUMBER *q1, NUMBER *q2)
{
        register NUMBER *r;
        NUMBER *q1tmp, *q2tmp, *q;
        ZVALUE res;

        if (qisfrac(q1) || qisfrac(q2)) {
                math_error("Non-integers for bitwise and");
                not_reached();
        }
        if (qcmp(q1, q2) == 0)
                return qlink(q1);
        if (qiszero(q1) || qiszero(q2))
                return qlink(&_qzero_);
        if (qisneg(q1)) {
                q1tmp = qcomp(q1);
                if (qisneg(q2)) {
                        q2tmp = qcomp(q2);
                        q = qor(q1tmp, q2tmp);
                        qfree(q1tmp);
                        qfree(q2tmp);
                        r = qcomp(q);
                        qfree(q);
                        return r;
                }
                r = qandnot(q2, q1tmp);
                qfree(q1tmp);
                return r;
        }
        if (qisneg(q2)) {
                q2tmp = qcomp(q2);
                r = qandnot(q1, q2tmp);
                qfree(q2tmp);
                return r;
        }
        zand(q1->num, q2->num, &res);
        if (ziszero(res)) {
                zfree(res);
                return qlink(&_qzero_);
        }
        r = qalloc();
        r->num = res;
        return r;
}


/*
 * Perform the bitwise XOR of two integers.
 */
NUMBER *
qxor(NUMBER *q1, NUMBER *q2)
{
        register NUMBER *r;
        NUMBER *q1tmp, *q2tmp, *q;
        ZVALUE res;

        if (qisfrac(q1) || qisfrac(q2)) {
                math_error("Non-integers for bitwise xor");
                not_reached();
        }
        if (qcmp(q1,q2) == 0)
                return qlink(&_qzero_);
        if (qiszero(q1))
                return qlink(q2);
        if (qiszero(q2))
                return qlink(q1);
        if (qisneg(q1)) {
                q1tmp = qcomp(q1);
                if (qisneg(q2)) {
                        q2tmp = qcomp(q2);
                        r = qxor(q1tmp, q2tmp);
                        qfree(q1tmp);
                        qfree(q2tmp);
                        return r;
                }
                q = qxor(q1tmp, q2);
                qfree(q1tmp);
                r = qcomp(q);
                qfree(q);
                return r;
        }
        if (qisneg(q2)) {
                q2tmp = qcomp(q2);
                q = qxor(q1, q2tmp);
                qfree(q2tmp);
                r = qcomp(q);
                qfree(q);
                return r;
        }
        zxor(q1->num, q2->num, &res);
        if (ziszero(res)) {
                zfree(res);
                return qlink(&_qzero_);
        }
        r = qalloc();
        r->num = res;
        return r;
}


/*
 * Perform the bitwise AND-NOT of two integers.
 */
NUMBER *
qandnot(NUMBER *q1, NUMBER *q2)
{
        register NUMBER *r;
        NUMBER *q1tmp, *q2tmp, *q;

        if (qisfrac(q1) || qisfrac(q2)) {
                math_error("Non-integers for bitwise xor");
                not_reached();
        }
        if (qcmp(q1,q2) == 0 || qiszero(q1))
                return qlink(&_qzero_);
        if (qiszero(q2))
                return qlink(q1);
        if (qisneg(q1)) {
                q1tmp = qcomp(q1);
                if (qisneg(q2)) {
                        q2tmp = qcomp(q2);
                        r = qandnot(q2tmp, q1tmp);
                        qfree(q1tmp);
                        qfree(q2tmp);
                        return r;
                }
                q = qor(q1tmp, q2);
                qfree(q1tmp);
                r = qcomp(q);
                qfree(q);
                return r;
        }
        if (qisneg(q2)) {
                q2tmp = qcomp(q2);
                r = qand(q1, q2tmp);
                qfree(q2tmp);
                return r;
        }
        r = qalloc();
        zandnot(q1->num, q2->num, &r->num);
        return r;
}

/*
 * Return the bitwise "complement" of a number.  This is - q -1 if q is an
 * integer, - q otherwise.
 */
NUMBER *
qcomp(NUMBER *q)
{
        NUMBER *qtmp;
        NUMBER *res;

        if (qiszero(q))
                return qlink(&_qnegone_);
        if (qisnegone(q))
                return qlink(&_qzero_);
        qtmp = qneg(q);
        if (qisfrac(q))
                return qtmp;
        res = qdec(qtmp);
        qfree(qtmp);
        return res;
}


/*
 * Return the number whose binary representation only has the specified
 * bit set (counting from zero).  This thus produces a given power of two.
 */
NUMBER *
qbitvalue(long n)
{
        register NUMBER *r;

        if (n == 0)
                return qlink(&_qone_);
        r = qalloc();
        if (n > 0)
                zbitvalue(n, &r->num);
        else
                zbitvalue(-n, &r->den);
        return r;
}

/*
 * Return 10^n
 */
NUMBER *
qtenpow(long n)
{
        register NUMBER *r;

        if (n == 0)
                return qlink(&_qone_);
        r = qalloc();
        if (n > 0)
                ztenpow(n, &r->num);
        else
                ztenpow(-n, &r->den);
        return r;
}


/*
 * Return the precision of a number (usually for examining an epsilon value).
 * The precision of a number e less than 1 is the positive
 * integer p for which e = 2^-p * f, where 1 <= f < 2.
 * Numbers greater than or equal to one have a precision of zero.
 * For example, the precision of e is 6 if 1/64 <= e < 1/32.
 */
long
qprecision(NUMBER *q)
{
        long r;

        if (qiszero(q) || qisneg(q)) {
                math_error("Non-positive number for precision");
                not_reached();
        }
        r = - qilog2(q);
        return (r < 0 ? 0 : r);
}


/*
 * Determine whether or not one number exactly divides another one.
 * Returns true if the first number is an integer multiple of the second one.
 */
bool
qdivides(NUMBER *q1, NUMBER *q2)
{
        if (qiszero(q1))
                return true;
        if (qisint(q1) && qisint(q2)) {
                if (qisunit(q2))
                        return true;
                return zdivides(q1->num, q2->num);
        }
        return zdivides(q1->num, q2->num) && zdivides(q2->den, q1->den);
}


/*
 * Compare two numbers and return an integer indicating their relative size.
 *      i = qrel(q1, q2);
 */
FLAG
qrel(NUMBER *q1, NUMBER *q2)
{
        ZVALUE z1, z2;
        long wc1, wc2;
        int sign;
        int z1f = 0, z2f = 0;

        if (q1 == q2)
                return 0;
        sign = q2->num.sign - q1->num.sign;
        if (sign)
                return sign;
        if (qiszero(q2))
                return !qiszero(q1);
        if (qiszero(q1))
                return -1;
        /*
         * Make a quick comparison by calculating the number of words
         * resulting as if we multiplied through by the denominators,
         * and then comparing the word counts.
         */
        sign = 1;
        if (qisneg(q1))
                sign = -1;
        wc1 = q1->num.len + q2->den.len;
        wc2 = q2->num.len + q1->den.len;
        if (wc1 < wc2 - 1)
                return -sign;
        if (wc2 < wc1 - 1)
                return sign;
        /*
         * Quick check failed, must actually do the full comparison.
         */
        if (zisunit(q2->den)) {
                z1 = q1->num;
        } else if (zisone(q1->num)) {
                z1 = q2->den;
        } else {
                z1f = 1;
                zmul(q1->num, q2->den, &z1);
        }
        if (zisunit(q1->den)) {
                z2 = q2->num;
        } else if (zisone(q2->num)) {
                z2 = q1->den;
        } else {
                z2f = 1;
                zmul(q2->num, q1->den, &z2);
        }
        sign = zrel(z1, z2);
        if (z1f)
                zfree(z1);
        if (z2f)
                zfree(z2);
        return sign;
}


/*
 * Compare two numbers to see if they are equal.
 * This differs from qrel in that the numbers are not ordered.
 * Returns true if they differ.
 */
bool
qcmp(NUMBER *q1, NUMBER *q2)
{
        if (q1 == q2)
                return false;
        if ((q1->num.sign != q2->num.sign) || (q1->num.len != q2->num.len) ||
                (q1->den.len != q2->den.len) || (*q1->num.v != *q2->num.v) ||
                (*q1->den.v != *q2->den.v))
                        return true;
        if (zcmp(q1->num, q2->num))
                return true;
        if (qisint(q1))
                return false;
        return zcmp(q1->den, q2->den);
}


/*
 * Compare a number against a normal small integer.
 * Returns 1, 0, or -1, according to whether the first number is greater,
 * equal, or less than the second number.
 *      res = qreli(q, n);
 */
FLAG
qreli(NUMBER *q, long n)
{
        ZVALUE z1, z2;
        FLAG res;

        if (qiszero(q))
                return ((n > 0) ? -1 : (n < 0));

        if (n == 0)
                return (q->num.sign ? -1 : 0);

        if (q->num.sign != (n < 0))
                return ((n < 0) ? 1 : -1);

        itoz(n, &z1);

        if (qisfrac(q)) {
                zmul(q->den, z1, &z2);
                zfree(z1);
                z1 = z2;
        }

        res = zrel(q->num, z1);
        zfree(z1);
        return res;
}


/*
 * Compare a number against a small integer to see if they are equal.
 * Returns true if they differ.
 */
bool
qcmpi(NUMBER *q, long n)
{
        long len;
#if LONG_BITS > BASEB
        FULL nf;
#endif

        len = q->num.len;
        if (qisfrac(q) || (q->num.sign != (n < 0)))
                return true;
        if (n < 0)
                n = -n;
        if (((HALF)(n)) != q->num.v[0])
                return true;
#if LONG_BITS > BASEB
        nf = ((FULL) n) >> BASEB;
        return ((nf != 0 || len > 1) && (len != 2 || nf != q->num.v[1]));
#else
        return (len > 1);
#endif
}


/*
 * Number node allocation routines
 */

#define NNALLOC 1000


STATIC NUMBER   *freeNum = NULL;
STATIC NUMBER   **firstNums = NULL;
STATIC long     blockcount = 0;


NUMBER *
qalloc(void)
{
        NUMBER *temp;
        NUMBER ** newfn;

        if (freeNum == NULL) {
                freeNum = (NUMBER *) malloc(sizeof (NUMBER) * NNALLOC);
                if (freeNum == NULL) {
                        math_error("Not enough memory");
                        not_reached();
                }
                freeNum[NNALLOC - 1].next = NULL;
                freeNum[NNALLOC - 1].links = 0;

                /*
                 * We prevent the temp pointer from walking behind freeNum
                 * by stopping one short of the end and running the loop one
                 * more time.
                 *
                 * We would stop the loop with just temp >= freeNum, but
                 * doing this helps make code checkers such as insure happy.
                 */
                for (temp = freeNum + NNALLOC - 2; temp > freeNum; --temp) {
                        temp->next = temp + 1;
                        temp->links = 0;
                }
                /* run the loop manually one last time */
                temp->next = temp + 1;
                temp->links = 0;

                blockcount++;
                if (firstNums == NULL) {
                    newfn = (NUMBER **) malloc(blockcount * sizeof(NUMBER *));
                } else {
                    newfn = (NUMBER **)
                            realloc(firstNums, blockcount * sizeof(NUMBER *));
                }
                if (newfn == NULL) {
                        math_error("Cannot allocate new number block");
                        not_reached();
                }
                firstNums = newfn;
                firstNums[blockcount - 1] = freeNum;
        }
        temp = freeNum;
        freeNum = temp->next;
        temp->links = 1;
        temp->num = _one_;
        temp->den = _one_;
        return temp;
}


void
qfreenum(NUMBER *q)
{
        if (q == NULL) {
                math_error("Calling qfreenum with null argument!!!");
                not_reached();
        }
        if (q->links != 0) {
                math_error("Calling qfreenum with non-zero links!!!");
                not_reached();
        }
        zfree(q->num);
        zfree(q->den);
        q->next = freeNum;
        freeNum = q;
}

void
shownumbers(void)
{
        NUMBER *vp;
        long i, j, k;
        long count = 0;

        printf("Index  Links  Digits           Value\n");
        printf("-----  -----  ------           -----\n");

        for (i = 0, k = 0; initnumbs[i] != NULL; i++) {
                count++;
                vp = initnumbs[i];
                printf("%6ld  %4ld  ", k++, vp->links);
                fitprint(vp, 40);
                printf("\n");
        }

        for (i = 0; i < blockcount; i++) {
                vp = firstNums[i];
                for (j = 0; j < NNALLOC; j++, k++, vp++) {
                        if (vp->links > 0) {
                                count++;
                                printf("%6ld  %4ld  ", k, vp->links);
                                fitprint(vp, 40);
                                printf("\n");
                        }
                }
        }
        printf("\nNumber: %ld\n", count);
}
