Usenet 1994 October/usenetsourcesnewsgroupsinfomagicoctober1994disk2.iso/unix/volume27/calc-2.9.0/part08

Text File | 1993-12-07 | 60KB | 2,761 lines

Newsgroups: comp.sources.unix
From: [e-mail] (David I. Bell)
Subject: v27i135: calc-2.9.0 - arbitrary precision C-like programmable calculator, Part08/19
References: <[e-mail]>
Sender: [e-mail]
Approved: [e-mail]

Submitted-By: [e-mail] (David I. Bell)
Posting-Number: Volume 27, Issue 135
Archive-Name: calc-2.9.0/part08

#!/bin/sh
# this is part 8 of a multipart archive
# do not concatenate these parts, unpack them in order with /bin/sh
# file calc2.9.0/opcodes.c continued
#
CurArch=8
if test ! -r s2_seq_.tmp
then echo "Please unpack part 1 first!"
     exit 1; fi
( read Scheck
  if test "$Scheck" != $CurArch
  then echo "Please unpack part $Scheck next!"
       exit 1;
  else exit 0; fi
) < s2_seq_.tmp || exit 1
echo "x - Continuing file calc2.9.0/opcodes.c"
sed 's/^X//' << 'SHAR_EOF' >> calc2.9.0/opcodes.c
X#endif
X    vsprintf(buf, fmt, ap);
X    va_end(ap);
X    fprintf(stderr, "%s\n", buf);
X    funcname = NULL;
X    longjmp(jmpbuf, 1);
X}
X
X/* END CODE */
SHAR_EOF
echo "File calc2.9.0/opcodes.c is complete"
chmod 0644 calc2.9.0/opcodes.c || echo "restore of calc2.9.0/opcodes.c fails"
set `wc -c calc2.9.0/opcodes.c`;Sum=$1
if test "$Sum" != "52101"
then echo original size 52101, current size $Sum;fi
echo "x - extracting calc2.9.0/opcodes.h (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/opcodes.h &&
X/*
X * Copyright (c) 1993 David I. Bell
X * Permission is granted to use, distribute, or modify this source,
X * provided that this copyright notice remains intact.
X */
X
X#ifndef    OPCODES_H
X#define    OPCODES_H
X
X
X/*
X * Opcodes
X */
X#define OP_NOP        0L    /* no operation */
X#define OP_LOCALADDR    1L    /* load address of local variable */
X#define OP_GLOBALADDR    2L    /* load address of global variable */
X#define OP_PARAMADDR    3L    /* load address of paramater variable */
X#define OP_LOCALVALUE    4L    /* load value of local variable */
X#define OP_GLOBALVALUE    5L    /* load value of global variable */
X#define OP_PARAMVALUE    6L    /* load value of paramater variable */
X#define OP_NUMBER    7L    /* load constant real numeric value */
X#define OP_INDEXADDR    8L    /* load array index address */
X#define    OP_PRINTRESULT    9L    /* print result of top-level expression */
X#define OP_ASSIGN    10L    /* assign value to variable */
X#define OP_ADD        11L    /* add top two values */
X#define OP_SUB        12L    /* subtract top two values */
X#define OP_MUL        13L    /* multiply top two values */
X#define OP_DIV        14L    /* divide top two values */
X#define OP_MOD        15L    /* take mod of top two values */
X#define OP_SAVE        16L    /* save value for later use */
X#define OP_NEGATE    17L    /* negate top value */
X#define OP_INVERT    18L    /* invert top value */
X#define OP_INT        19L    /* take integer part of top value */
X#define OP_FRAC        20L    /* take fraction part of top value */
X#define OP_NUMERATOR    21L    /* take numerator of top value */
X#define OP_DENOMINATOR    22L    /* take denominator of top value */
X#define OP_DUPLICATE    23L    /* duplicate top value on stack */
X#define OP_POP        24L    /* pop top value from stack */
X#define OP_RETURN    25L    /* return value of function */
X#define OP_JUMPEQ    26L    /* jump if top value is zero */
X#define OP_JUMPNE    27L    /* jump if top value is nonzero */
X#define OP_JUMP        28L    /* jump unconditionally */
X#define OP_USERCALL    29L    /* call a user-defined function */
X#define OP_GETVALUE    30L    /* convert address to value */
X#define OP_EQ        31L    /* test top two elements for equality */
X#define OP_NE        32L    /* test top two elements for inequality */
X#define OP_LE        33L    /* test top two elements for <= */
X#define OP_GE        34L    /* test top two elements for >= */
X#define OP_LT        35L    /* test top two elements for < */
X#define OP_GT        36L    /* test top two elements for > */
X#define OP_PREINC    37L    /* add one to variable (++x) */
X#define OP_PREDEC    38L    /* subtract one from variable (--x) */
X#define OP_POSTINC    39L    /* add one to variable (x++) */
X#define OP_POSTDEC    40L    /* subtract one from variable (x--) */
X#define OP_DEBUG    41L    /* debugging point */
X#define OP_PRINT    42L    /* print value */
X#define OP_ASSIGNPOP    43L    /* assign to variable and remove it */
X#define OP_ZERO        44L    /* put zero on the stack */
X#define OP_ONE        45L    /* put one on the stack */
X#define OP_PRINTEOL    46L    /* print end of line */
X#define OP_PRINTSPACE    47L    /* print a space */
X#define OP_PRINTSTRING    48L    /* print constant string */
X#define OP_DUPVALUE    49L    /* duplicate value of top value */
X#define OP_OLDVALUE    50L    /* old calculation value */
X#define OP_QUO        51L    /* integer quotient of top two values */
X#define OP_POWER    52L    /* number raised to a power */
X#define OP_QUIT        53L    /* quit program */
X#define OP_CALL        54L    /* call built-in routine */
X#define OP_GETEPSILON    55L    /* get allowed error for calculations */
X#define OP_AND        56L    /* arithmetic and */
X#define OP_OR        57L    /* arithmetic or */
X#define OP_NOT        58L    /* logical not */
X#define OP_ABS        59L    /* absolute value */
X#define OP_SGN        60L    /* sign of number */
X#define OP_ISINT    61L    /* whether top value is integer */
X#define OP_CONDORJUMP    62L    /* conditional or jump */
X#define OP_CONDANDJUMP    63L    /* conditional and jump */
X#define OP_SQUARE    64L    /* square top value */
X#define OP_STRING    65L    /* load constant string value */
X#define OP_ISNUM    66L    /* whether top value is a number */
X#define OP_UNDEF    67L    /* load undefined value on stack */
X#define OP_ISNULL    68L    /* whether variable is the null value */
X#define OP_ARGVALUE    69L    /* load value of argument (parameter) n */
X#define OP_MATCREATE    70L    /* create matrix */
X#define OP_ISMAT    71L    /* whether variable is a matrix */
X#define OP_ISSTR    72L    /* whether variable is a string */
X#define OP_GETCONFIG    73L    /* get value of configuration parameter */
X#define OP_LEFTSHIFT    74L    /* left shift of integer */
X#define OP_RIGHTSHIFT    75L    /* right shift of integer */
X#define OP_CASEJUMP    76L    /* test case and jump if not matched */
X#define OP_ISODD    77L    /* whether value is an odd integer */
X#define OP_ISEVEN    78L    /* whether value is even integer */
X#define OP_FIADDR    79L    /* 'fast index' matrix value address */
X#define OP_FIVALUE    80L    /* 'fast index' matrix value */
X#define OP_ISREAL    81L    /* test value for real number */
X#define OP_IMAGINARY    82L    /* load imaginary numeric constant */
X#define OP_RE        83L    /* real part of complex number */
X#define OP_IM        84L    /* imaginary part of complex number */
X#define OP_CONJUGATE    85L    /* complex conjugate of complex number */
X#define OP_OBJCREATE    86L    /* create object */
X#define OP_ISOBJ    87L    /* whether value is an object */
X#define OP_NORM        88L    /* norm of value (square of abs) */
X#define OP_ELEMADDR    89L    /* address of element of object */
X#define OP_ELEMVALUE    90L    /* value of element of object */
X#define OP_ISTYPE    91L    /* whether two values are the same type */
X#define OP_SCALE    92L    /* scale value by a power of two */
X#define    OP_ISLIST    93L    /* whether value is a list */
X#define    OP_SWAP        94L    /* swap values of two variables */
X#define    OP_ISSIMPLE    95L    /* whether value is a simple type */
X#define    OP_CMP        96L    /* compare values returning -1, 0, or 1 */
X#define    OP_QUOMOD    97L    /* calculate quotient and remainder */
X#define    OP_SETCONFIG    98L    /* set configuration parameter */
X#define    OP_SETEPSILON    99L    /* set allowed error for calculations */
X#define    OP_ISFILE    100L    /* whether value is a file */
X#define    OP_ISASSOC    101L    /* whether value is an association */
X#define    OP_INITSTATIC    102L    /* once only code for static initialization */
X#define    OP_ELEMINIT    103L    /* assign element of matrix or object */
X#define MAX_OPCODE    103L    /* highest legal opcode */
X
X#endif
X
X/* END CODE */
SHAR_EOF
chmod 0644 calc2.9.0/opcodes.h || echo "restore of calc2.9.0/opcodes.h fails"
set `wc -c calc2.9.0/opcodes.h`;Sum=$1
if test "$Sum" != "6052"
then echo original size 6052, current size $Sum;fi
echo "x - extracting calc2.9.0/qfunc.c (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/qfunc.c &&
X/*
X * Copyright (c) 1993 David I. Bell
X * Permission is granted to use, distribute, or modify this source,
X * provided that this copyright notice remains intact.
X *
X * Extended precision rational arithmetic non-primitive functions
X */
X
X#include "qmath.h"
X
X
XNUMBER *_epsilon_;    /* default precision for real functions */
Xlong _epsilonprec_;    /* bits of precision for epsilon */
X
X
X/*
X * Set the default precision for real calculations.
X * The precision must be between zero and one.
X */
Xvoid
Xsetepsilon(q)
X    NUMBER *q;        /* number to be set as the new epsilon */
X{
X    NUMBER *old;
X
X    if (qisneg(q) || qiszero(q) || (qreli(q, 1L) >= 0))
X        math_error("Epsilon value must be between zero and one");
X    old = _epsilon_;
X    _epsilonprec_ = qprecision(q);
X    _epsilon_ = qlink(q);
X    if (old)
X        qfree(old);
X}
X
X
X/*
X * Return the inverse of one number modulo another.
X * That is, find x such that:
X *    Ax = 1 (mod B)
X * Returns zero if the numbers are not relatively prime (temporary hack).
X */
XNUMBER *
Xqminv(q1, q2)
X    NUMBER *q1, *q2;
X{
X    NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integers for minv");
X    r = qalloc();
X    if (zmodinv(q1->num, q2->num, &r->num)) {
X        qfree(r);
X        return qlink(&_qzero_);
X    }
X    return r;
X}
X
X
X/*
X * Return the modulo of one number raised to another.
X * Here q1 is the number to be raised, q2 is the power to raise it to,
X * and q3 is the number to take the modulo with the result.
X * The second and third numbers are assumed nonnegative.
X * Returned answer is non-negative.
X *    q4 = qpowermod(q1, q2, q3);
X */
XNUMBER *
Xqpowermod(q1, q2, q3)
X    NUMBER *q1, *q2, *q3;
X{
X    NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2) || qisfrac(q3))
X        math_error("Non-integers for powermod");
X    r = qalloc();
X    zpowermod(q1->num, q2->num, q3->num, &r->num);
X    return r;
X}
X
X
X/*
X * Return the power function of one number with another.
X * The power must be integral.
X *    q3 = qpowi(q1, q2);
X */
XNUMBER *
Xqpowi(q1, q2)
X    NUMBER *q1, *q2;
X{
X    register NUMBER *r;
X    BOOL invert, sign;
X    ZVALUE num, den, z2;
X
X    if (qisfrac(q2))
X        math_error("Raising number to fractional power");
X    num = q1->num;
X    den = q1->den;
X    z2 = q2->num;
X    sign = (num.sign && zisodd(z2));
X    invert = z2.sign;
X    num.sign = 0;
X    z2.sign = 0;
X    /*
X    * Check for trivial cases first.
X    */
X    if (ziszero(num)) {    /* zero raised to a power */
X        if (invert || ziszero(z2))
X            math_error("Zero raised to non-positive power");
X        return qlink(&_qzero_);
X    }
X    if (zisunit(num) && zisunit(den)) {    /* 1 or -1 raised to a power */
X        r = (sign ? q1 : &_qone_);
X        r->links++;
X        return r;
X    }
X    if (ziszero(z2))    /* raising to zeroth power */
X        return qlink(&_qone_);
X    if (zisunit(z2)) {    /* raising to power 1 or -1 */
X        if (invert)
X            return qinv(q1);
X        return qlink(q1);
X    }
X    /*
X     * Not a trivial case.  Do the real work.
X     */
X    r = qalloc();
X    if (!zisunit(num))
X        zpowi(num, z2, &r->num);
X    if (!zisunit(den))
X        zpowi(den, z2, &r->den);
X    if (invert) {
X        z2 = r->num;
X        r->num = r->den;
X        r->den = z2;
X    }
X    r->num.sign = sign;
X    return r;
X}
X
X
X/*
X * Given the legs of a right triangle, compute its hypothenuse within
X * the specified error.  This is sqrt(a^2 + b^2).
X */
XNUMBER *
Xqhypot(q1, q2, epsilon)
X    NUMBER *q1, *q2, *epsilon;
X{
X    NUMBER *tmp1, *tmp2, *tmp3;
X
X    if (qisneg(epsilon) || qiszero(epsilon))
X        math_error("Bad epsilon value for hypot");
X    if (qiszero(q1))
X        return qabs(q2);
X    if (qiszero(q2))
X        return qabs(q1);
X    tmp1 = qsquare(q1);
X    tmp2 = qsquare(q2);
X    tmp3 = qadd(tmp1, tmp2);
X    qfree(tmp1);
X    qfree(tmp2);
X    tmp1 = qsqrt(tmp3, epsilon);
X    qfree(tmp3);
X    return tmp1;
X}
X
X
X/*
X * Given one leg of a right triangle with unit hypothenuse, calculate
X * the other leg within the specified error.  This is sqrt(1 - a^2).
X * If the wantneg flag is nonzero, then negative square root is returned.
X */
XNUMBER *
Xqlegtoleg(q, epsilon, wantneg)
X    NUMBER *q, *epsilon;
X    BOOL wantneg;
X{
X    NUMBER *qt, *res, qtmp;
X    ZVALUE num, ztmp1, ztmp2;
X
X    if (qisneg(epsilon) || qiszero(epsilon))
X        math_error("Bad epsilon value for legtoleg");
X    if (qisunit(q))
X        return qlink(&_qzero_);
X    if (qiszero(q)) {
X        if (wantneg)
X            return qlink(&_qnegone_);
X        return qlink(&_qone_);
X    }
X    num = q->num;
X    num.sign = 0;
X    if (zrel(num, q->den) >= 0)
X        math_error("Leg too large in legtoleg");
X    zsquare(q->den, &ztmp1);
X    zsquare(num, &ztmp2);
X    zsub(ztmp1, ztmp2, &qtmp.num);
X    zfree(ztmp1);
X    zfree(ztmp2);
X    qtmp.den = _one_;
X    qt = qsqrt(&qtmp, epsilon);
X    zfree(qtmp.num);
X    qtmp.num = q->den;
X    res = qdiv(qt, &qtmp);
X    qfree(qt);
X    qt = qbappr(res, epsilon);
X    qfree(res);
X    if (wantneg) {
X        res = qneg(qt);
X        qfree(qt);
X        qt = res;
X    }
X    return qt;
X}
X
X
X/*
X * Compute the square root of a number to within the specified error.
X * If the number is an exact square, the exact result is returned.
X *    q3 = qsqrt(q1, q2);
X */
XNUMBER *
Xqsqrt(q1, epsilon)
X    register NUMBER *q1, *epsilon;
X{
X    long bits, bits2;    /* number of bits of precision */
X    int exact;
X    NUMBER *r;
X    ZVALUE t1, t2;
X
X    if (qisneg(q1))
X        math_error("Square root of negative number");
X    if (qisneg(epsilon) || qiszero(epsilon))
X        math_error("Bad epsilon value for sqrt");
X    if (qiszero(q1))
X        return qlink(&_qzero_);
X    if (qisunit(q1))
X        return qlink(&_qone_);
X    if (qiszero(epsilon) && qisint(q1) && zistiny(q1->num) && (*q1->num.v <= 3))
X        return qlink(&_qone_);
X    bits = zhighbit(epsilon->den) - zhighbit(epsilon->num) + 1;
X    if (bits < 0)
X        bits = 0;
X    bits2 = zhighbit(q1->num) - zhighbit(q1->den) + 1;
X    if (bits2 > 0)
X        bits += bits2;
X    r = qalloc();
X    zshift(q1->num, bits * 2, &t2);
X    zmul(q1->den, t2, &t1);
X    zfree(t2);
X    exact = zsqrt(t1, &t2);
X    zfree(t1);
X    if (exact) {
X        zshift(q1->den, bits, &t1);
X        zreduce(t2, t1, &r->num, &r->den);
X    } else {
X        zquo(t2, q1->den, &t1);
X        zfree(t2);
X        zbitvalue(bits, &t2);
X        zreduce(t1, t2, &r->num, &r->den);
X    }
X    zfree(t1);
X    zfree(t2);
X    if (qiszero(r)) {
X        qfree(r);
X        r = qlink(&_qzero_);
X    }
X    return r;
X}
X
X
X/*
X * Calculate the integral part of the square root of a number.
X * Example:  qisqrt(13) = 3.
X */
XNUMBER *
Xqisqrt(q)
X    NUMBER *q;
X{
X    NUMBER *r;
X    ZVALUE tmp;
X
X    if (qisneg(q))
X        math_error("Square root of negative number");
X    if (qiszero(q))
X        return qlink(&_qzero_);
X    if (qisint(q) && zistiny(q->num) && (z1tol(q->num) < 4))
X        return qlink(&_qone_);
X    r = qalloc();
X    if (qisint(q)) {
X        (void) zsqrt(q->num, &r->num);
X        return r;
X    }
X    zquo(q->num, q->den, &tmp);
X    (void) zsqrt(tmp, &r->num);
X    zfree(tmp);
X    return r;
X}
X
X
X/*
X * Return whether or not a number is an exact square.
X */
XBOOL
Xqissquare(q)
X    NUMBER *q;
X{
X    BOOL flag;
X
X    flag = zissquare(q->num);
X    if (qisint(q) || !flag)
X        return flag;
X    return zissquare(q->den);
X}
X
X
X/*
X * Compute the greatest integer of the Kth root of a number.
X * Example:  qiroot(85, 3) = 4.
X */
XNUMBER *
Xqiroot(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER *r;
X    ZVALUE tmp;
X
X    if (qisneg(q2) || qiszero(q2) || qisfrac(q2))
X        math_error("Taking number to bad root value");
X    if (qiszero(q1))
X        return qlink(&_qzero_);
X    if (qisone(q1) || qisone(q2))
X        return qlink(q1);
X    if (qistwo(q2))
X        return qisqrt(q1);
X    r = qalloc();
X    if (qisint(q1)) {
X        zroot(q1->num, q2->num, &r->num);
X        return r;
X    }
X    zquo(q1->num, q1->den, &tmp);
X    zroot(tmp, q2->num, &r->num);
X    zfree(tmp);
X    return r;
X}
X
X
X/*
X * Return the greatest integer of the base 2 log of a number.
X * This is the number such that  1 <= x / log2(x) < 2.
X * Examples:  qilog2(8) = 3, qilog2(1.3) = 1, qilog2(1/7) = -3.
X */
Xlong
Xqilog2(q)
X    NUMBER *q;        /* number to take log of */
X{
X    long n;            /* power of two */
X    int c;            /* result of comparison */
X    ZVALUE tmp;        /* temporary value */
X
X    if (qisneg(q) || qiszero(q))
X        math_error("Non-positive number for log2");
X    if (qisint(q))
X        return zhighbit(q->num);
X    n = zhighbit(q->num) - zhighbit(q->den);
X    if (n == 0)
X        c = zrel(q->num, q->den);
X    else if (n > 0) {
X        zshift(q->den, n, &tmp);
X        c = zrel(q->num, tmp);
X    } else {
X        zshift(q->num, n, &tmp);
X        c = zrel(tmp, q->den);
X    }
X    if (n)
X        zfree(tmp);
X    if (c < 0)
X        n--;
X    return n;
X}
X
X
X/*
X * Return the greatest integer of the base 10 log of a number.
X * This is the number such that  1 <= x / log10(x) < 10.
X * Examples:  qilog10(100) = 2, qilog10(12.3) = 1, qilog10(.023) = -2.
X */
Xlong
Xqilog10(q)
X    NUMBER *q;        /* number to take log of */
X{
X    long n;            /* log value */
X    ZVALUE temp;        /* temporary value */
X
X    if (qisneg(q) || qiszero(q))
X        math_error("Non-positive number for log10");
X    if (qisint(q))
X        return zlog10(q->num);
X    /*
X     * The number is not an integer.
X     * Compute the result if the number is greater than one.
X     */
X    if ((q->num.len > q->den.len) ||
X        ((q->num.len == q->den.len) && (zrel(q->num, q->den) > 0))) {
X            zquo(q->num, q->den, &temp);
X            n = zlog10(temp);
X            zfree(temp);
X            return n;
X    }
X    /*
X     * Here if the number is less than one.
X     * If the number is the inverse of a power of ten, then the obvious answer
X     * will be off by one.  Subtracting one if the number is the inverse of an
X     * integer will fix it.
X     */
X    if (zisunit(q->num))
X        zsub(q->den, _one_, &temp);
X    else
X        zquo(q->den, q->num, &temp);
X    n = -zlog10(temp) - 1;
X    zfree(temp);
X    return n;
X}
X
X
X/*
X * Return the number of digits in a number, ignoring the sign.
X * For fractions, this is the number of digits of its greatest integer.
X * Examples: qdigits(3456) = 4, qdigits(-23.45) = 2, qdigits(.0120) = 1.
X */
Xlong
Xqdigits(q)
X    NUMBER *q;        /* number to count digits of */
X{
X    long n;            /* number of digits */
X    ZVALUE temp;        /* temporary value */
X
X    if (qisint(q))
X        return zdigits(q->num);
X    zquo(q->num, q->den, &temp);
X    n = zdigits(temp);
X    zfree(temp);
X    return n;
X}
X
X
X/*
X * Return the digit at the specified decimal place of a number represented
X * in floating point.  The lowest digit of the integral part of a number
X * is the zeroth decimal place.  Negative decimal places indicate digits
X * to the right of the decimal point.  Examples: qdigit(1234.5678, 1) = 3,
X * qdigit(1234.5678, -3) = 7.
X */
XFLAG
Xqdigit(q, n)
X    NUMBER *q;
X    long n;
X{
X    ZVALUE tenpow, tmp1, tmp2;
X    FLAG res;
X
X    /*
X     * Zero number or negative decimal place of integer is trivial.
X     */
X    if (qiszero(q) || (qisint(q) && (n < 0)))
X        return 0;
X    /*
X     * For non-negative decimal places, answer is easy.
X     */
X    if (n >= 0) {
X        if (qisint(q))
X            return zdigit(q->num, n);
X        zquo(q->num, q->den, &tmp1);
X        res = zdigit(tmp1, n);
X        zfree(tmp1);
X        return res;
X    }
X    /*
X     * Fractional value and want negative digit, must work harder.
X     */
X    ztenpow(-n, &tenpow);
X    zmul(q->num, tenpow, &tmp1);
X    zfree(tenpow);
X    zquo(tmp1, q->den, &tmp2);
X    res = zmodi(tmp2, 10L);
X    zfree(tmp1);
X    zfree(tmp2);
X    return res;
X}
X
X
X/*
X * Return whether or not a bit is set at the specified bit position in a
X * number.  The lowest bit of the integral part of a number is the zeroth
X * bit position.  Negative bit positions indicate bits to the right of the
X * binary decimal point.  Examples: qdigit(17.1, 0) = 1, qdigit(17.1, -1) = 0.
X */
XBOOL
Xqisset(q, n)
X    NUMBER *q;
X    long n;
X{
X    NUMBER *qtmp1, *qtmp2;
X    ZVALUE ztmp;
X    BOOL res;
X
X    /*
X     * Zero number or negative bit position place of integer is trivial.
X     */
X    if (qiszero(q) || (qisint(q) && (n < 0)))
X        return FALSE;
X    /*
X     * For non-negative bit positions, answer is easy.
X     */
X    if (n >= 0) {
X        if (qisint(q))
X            return zisset(q->num, n);
X        zquo(q->num, q->den, &ztmp);
X        res = zisset(ztmp, n);
X        zfree(ztmp);
X        return res;
X    }
X    /*
X     * Fractional value and want negative bit position, must work harder.
X     */
X    qtmp1 = qscale(q, -n);
X    qtmp2 = qint(qtmp1);
X    qfree(qtmp1);
X    res = ((qtmp2->num.v[0] & 0x01) != 0);
X    qfree(qtmp2);
X    return res;
X}
X
X
X/*
X * Compute the factorial of an integer.
X *    q2 = qfact(q1);
X */
XNUMBER *
Xqfact(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisfrac(q))
X        math_error("Non-integral factorial");
X    if (qiszero(q) || zisone(q->num))
X        return qlink(&_qone_);
X    r = qalloc();
X    zfact(q->num, &r->num);
X    return r;
X}
X
X
X/*
X * Compute the product of the primes less than or equal to a number.
X *    q2 = qpfact(q1);
X */
XNUMBER *
Xqpfact(q)
X    register NUMBER *q;
X{
X    NUMBER *r;
X
X    if (qisfrac(q))
X        math_error("Non-integral factorial");
X    r = qalloc();
X    zpfact(q->num, &r->num);
X    return r;
X}
X
X
X/*
X * Compute the lcm of all the numbers less than or equal to a number.
X *    q2 = qlcmfact(q1);
X */
XNUMBER *
Xqlcmfact(q)
X    register NUMBER *q;
X{
X    NUMBER *r;
X
X    if (qisfrac(q))
X        math_error("Non-integral lcmfact");
X    r = qalloc();
X    zlcmfact(q->num, &r->num);
X    return r;
X}
X
X
X/*
X * Compute the permutation function  M! / (M - N)!.
X */
XNUMBER *
Xqperm(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    register NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integral arguments for permutation");
X    r = qalloc();
X    zperm(q1->num, q2->num, &r->num);
X    return r;
X}
X
X
X/*
X * Compute the combinatorial function  M! / (N! * (M - N)!).
X */
XNUMBER *
Xqcomb(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    register NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integral arguments for combinatorial");
X    r = qalloc();
X    zcomb(q1->num, q2->num, &r->num);
X    return r;
X}
X
X
X/*
X * Compute the Jacobi function (a / b).
X * -1 => a is not quadratic residue mod b
X * 1 => b is composite, or a is quad residue of b
X * 0 => b is even or b < 0
X */
XNUMBER *
Xqjacobi(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integral arguments for jacobi");
X    return itoq((long) zjacobi(q1->num, q2->num));
X}
X
X
X/*
X * Compute the Fibonacci number F(n).
X */
XNUMBER *
Xqfib(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisfrac(q))
X        math_error("Non-integral Fibonacci number");
X    r = qalloc();
X    zfib(q->num, &r->num);
X    return r;
X}
X
X
X/*
X * Truncate a number to the specified number of decimal places.
X * Specifying zero places makes the result identical to qint.
X * Example: qtrunc(2/3, 3) = .666
X */
XNUMBER *
Xqtrunc(q1, q2)
X    NUMBER *q1, *q2;
X{
X    long places;
X    NUMBER *r;
X    ZVALUE tenpow, tmp1, tmp2;
X
X    if (qisfrac(q2) || qisneg(q2) || !zistiny(q2->num))
X        math_error("Bad number of places for qtrunc");
X    if (qisint(q1))
X        return qlink(q1);
X    r = qalloc();
X    places = z1tol(q2->num);
X    /*
X     * Ok, produce the result.
X     * First see if we want no places, in which case just take integer part.
X     */
X    if (places == 0) {
X        zquo(q1->num, q1->den, &r->num);
X        return r;
X    }
X    ztenpow(places, &tenpow);
X    zmul(q1->num, tenpow, &tmp1);
X    zquo(tmp1, q1->den, &tmp2);
X    zfree(tmp1);
X    if (ziszero(tmp2)) {
X        zfree(tmp2);
X        return qlink(&_qzero_);
X    }
X    /*
X     * Now reduce the result to the lowest common denominator.
X     */
X    zgcd(tmp2, tenpow, &tmp1);
X    if (zisunit(tmp1)) {
X        zfree(tmp1);
X        r->num = tmp2;
X        r->den = tenpow;
X        return r;
X    }
X    zquo(tmp2, tmp1, &r->num);
X    zquo(tenpow, tmp1, &r->den);
X    zfree(tmp1);
X    zfree(tmp2);
X    zfree(tenpow);
X    return r;
X}
X
X
X/*
X * Round a number to the specified number of decimal places.
X * Zero decimal places means round to the nearest integer.
X * Example: qround(2/3, 3) = .667
X */
XNUMBER *
Xqround(q, places)
X    NUMBER *q;        /* number to be rounded */
X    long places;        /* number of decimal places to round to */
X{
X    NUMBER *r;
X    ZVALUE tenpow, roundval, tmp1, tmp2;
X
X    if (places < 0)
X        math_error("Negative places for qround");
X    if (qisint(q))
X        return qlink(q);
X    /*
X     * Calculate one half of the denominator, ignoring fractional results.
X     * This is the value we will add in order to cause rounding.
X     */
X    zshift(q->den, -1L, &roundval);
X    roundval.sign = q->num.sign;
X    /*
X     * Ok, now do the actual work to produce the result.
X     */
X    r = qalloc();
X    ztenpow(places, &tenpow);
X    zmul(q->num, tenpow, &tmp2);
X    zadd(tmp2, roundval, &tmp1);
X    zfree(tmp2);
X    zfree(roundval);
X    zquo(tmp1, q->den, &tmp2);
X    zfree(tmp1);
X    if (ziszero(tmp2)) {
X        zfree(tmp2);
X        return qlink(&_qzero_);
X    }
X    /*
X     * Now reduce the result to the lowest common denominator.
X     */
X    zgcd(tmp2, tenpow, &tmp1);
X    if (zisunit(tmp1)) {
X        zfree(tmp1);
X        r->num = tmp2;
X        r->den = tenpow;
X        return r;
X    }
X    zquo(tmp2, tmp1, &r->num);
X    zquo(tenpow, tmp1, &r->den);
X    zfree(tmp1);
X    zfree(tmp2);
X    zfree(tenpow);
X    return r;
X}
X
X
X/*
X * Truncate a number to the specified number of binary places.
X * Specifying zero places makes the result identical to qint.
X */
XNUMBER *
Xqbtrunc(q1, q2)
X    NUMBER *q1, *q2;
X{
X    long places, twopow;
X    NUMBER *r;
X    ZVALUE tmp1, tmp2;
X
X    if (qisfrac(q2) || qisneg(q2) || !zistiny(q2->num))
X        math_error("Bad number of places for qtrunc");
X    if (qisint(q1))
X        return qlink(q1);
X    r = qalloc();
X    places = z1tol(q2->num);
X    /*
X     * Ok, produce the result.
X     * First see if we want no places, in which case just take integer part.
X     */
X    if (places == 0) {
X        zquo(q1->num, q1->den, &r->num);
X        return r;
X    }
X    zshift(q1->num, places, &tmp1);
X    zquo(tmp1, q1->den, &tmp2);
X    zfree(tmp1);
X    if (ziszero(tmp2)) {
X        zfree(tmp2);
X        return qlink(&_qzero_);
X    }
X    /*
X     * Now reduce the result to the lowest common denominator.
X     */
X    if (zisodd(tmp2)) {
X        r->num = tmp2;
X        zbitvalue(places, &r->den);
X        return r;
X    }
X    twopow = zlowbit(tmp2);
X    if (twopow > places)
X        twopow = places;
X    places -= twopow;
X    zshift(tmp2, -twopow, &r->num);
X    zfree(tmp2);
X    zbitvalue(places, &r->den);
X    return r;
X}
X
X
X/*
X * Round a number to the specified number of binary places.
X * Zero binary places means round to the nearest integer.
X */
XNUMBER *
Xqbround(q, places)
X    NUMBER *q;        /* number to be rounded */
X    long places;        /* number of binary places to round to */
X{
X    long twopow;
X    NUMBER *r;
X    ZVALUE roundval, tmp1, tmp2;
X
X    if (places < 0)
X        math_error("Negative places for qbround");
X    if (qisint(q))
X        return qlink(q);
X    r = qalloc();
X    /*
X     * Calculate one half of the denominator, ignoring fractional results.
X     * This is the value we will add in order to cause rounding.
X     */
X    zshift(q->den, -1L, &roundval);
X    roundval.sign = q->num.sign;
X    /*
X     * Ok, produce the result.
X     */
X    zshift(q->num, places, &tmp1);
X    zadd(tmp1, roundval, &tmp2);
X    zfree(roundval);
X    zfree(tmp1);
X    zquo(tmp2, q->den, &tmp1);
X    zfree(tmp2);
X    if (ziszero(tmp1)) {
X        zfree(tmp1);
X        return qlink(&_qzero_);
X    }
X    /*
X     * Now reduce the result to the lowest common denominator.
X     */
X    if (zisodd(tmp1)) {
X        r->num = tmp1;
X        zbitvalue(places, &r->den);
X        return r;
X    }
X    twopow = zlowbit(tmp1);
X    if (twopow > places)
X        twopow = places;
X    places -= twopow;
X    zshift(tmp1, -twopow, &r->num);
X    zfree(tmp1);
X    zbitvalue(places, &r->den);
X    return r;
X}
X
X
X/*
X * Approximate a number by using binary rounding with the minimum number
X * of binary places so that the resulting number is within the specified
X * epsilon of the original number.
X */
XNUMBER *
Xqbappr(q, e)
X    NUMBER *q, *e;
X{
X    long bits;
X
X    if (qisneg(e) || qiszero(e))
X        math_error("Bad epsilon value for qbappr");
X    if (e == _epsilon_)
X        bits = _epsilonprec_ + 1;
X    else
X        bits = qprecision(e) + 1;
X    return qbround(q, bits);
X}
X
X
X/*
X * Approximate a number using continued fractions until the approximation
X * error is less than the specified value.  If a NULL pointer is given
X * for the error value, then the closest simpler fraction is returned.
X */
XNUMBER *
Xqcfappr(q, e)
X    NUMBER *q, *e;
X{
X    NUMBER qtest, *qtmp;
X    ZVALUE u1, u2, u3, v1, v2, v3, t1, t2, t3, qq, tt;
X    int i;
X    BOOL haveeps;
X
X    haveeps = TRUE;
X    if (e == NULL) {
X        haveeps = FALSE;
X        e = &_qzero_;
X    }
X    if (qisneg(e))
X        math_error("Negative epsilon for cfappr");
X    if (qisint(q) || zisunit(q->num) || (haveeps && qiszero(e)))
X        return qlink(q);
X    u1 = _one_;
X    u2 = _zero_;
X    u3 = q->num;
X    u3.sign = 0;
X    v1 = _zero_;
X    v2 = _one_;
X    v3 = q->den;
X    while (!ziszero(v3)) {
X        if (!ziszero(u2) && !ziszero(u1)) {
X            qtest.num = u2;
X            qtest.den = u1;
X            qtest.den.sign = 0;
X            qtest.num.sign = q->num.sign;
X            qtmp = qsub(q, &qtest);
X            qtest = *qtmp;
X            qtest.num.sign = 0;
X            i = qrel(&qtest, e);
X            qfree(qtmp);
X            if (i <= 0)
X                break;
X        }
X        zquo(u3, v3, &qq);
X        zmul(qq, v1, &tt); zsub(u1, tt, &t1); zfree(tt);
X        zmul(qq, v2, &tt); zsub(u2, tt, &t2); zfree(tt);
X        zmul(qq, v3, &tt); zsub(u3, tt, &t3); zfree(tt);
X        zfree(qq); zfree(u1); zfree(u2);
X        if ((u3.v != q->num.v) && (u3.v != q->den.v))
X            zfree(u3);
X        u1 = v1; u2 = v2; u3 = v3;
X        v1 = t1; v2 = t2; v3 = t3;
X    }
X    if (u3.v != q->den.v)
X        zfree(u3);
X    zfree(v1);
X    zfree(v2);
X    i = ziszero(v3);
X    zfree(v3);
X    if (i && haveeps) {
X        zfree(u1);
X        zfree(u2);
X        return qlink(q);
X    }
X    qtest.num = u2;
X    qtest.den = u1;
X    qtest.den.sign = 0;
X    qtest.num.sign = q->num.sign;
X    qtmp = qcopy(&qtest);
X    zfree(u1);
X    zfree(u2);
X    return qtmp;
X}
X
X
X/*
X * Return an indication on whether or not two fractions are approximately
X * equal within the specified epsilon. Returns negative if the absolute value
X * of the difference between the two numbers is less than epsilon, zero if
X * the difference is equal to epsilon, and positive if the difference is
X * greater than epsilon.
X */
XFLAG
Xqnear(q1, q2, epsilon)
X    NUMBER *q1, *q2, *epsilon;
X{
X    int res;
X    NUMBER qtemp, *qq;
X
X    if (qisneg(epsilon))
X        math_error("Negative epsilon for near");
X    if (q1 == q2) {
X        if (qiszero(epsilon))
X            return 0;
X        return -1;
X    }
X    if (qiszero(epsilon))
X        return qcmp(q1, q2);
X    if (qiszero(q2)) {
X        qtemp = *q1;
X        qtemp.num.sign = 0;
X        return qrel(&qtemp, epsilon);
X    }
X    if (qiszero(q1)) {
X        qtemp = *q2;
X        qtemp.num.sign = 0;
X        return qrel(&qtemp, epsilon);
X    }
X    qq = qsub(q1, q2);
X    qtemp = *qq;
X    qtemp.num.sign = 0;
X    res = qrel(&qtemp, epsilon);
X    qfree(qq);
X    return res;
X}
X
X
X/*
X * Compute the gcd (greatest common divisor) of two numbers.
X *    q3 = qgcd(q1, q2);
X */
XNUMBER *
Xqgcd(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    ZVALUE z;
X    NUMBER *q;
X
X    if (q1 == q2)
X        return qabs(q1);
X    if (qisfrac(q1) || qisfrac(q2)) {
X        q = qalloc();
X        zgcd(q1->num, q2->num, &q->num);
X        zlcm(q1->den, q2->den, &q->den);
X        return q;
X    }
X    if (qiszero(q1))
X        return qabs(q2);
X    if (qiszero(q2))
X        return qabs(q1);
X    if (qisunit(q1) || qisunit(q2))
X        return qlink(&_qone_);
X    zgcd(q1->num, q2->num, &z);
X    if (zisunit(z)) {
X        zfree(z);
X        return qlink(&_qone_);
X    }
X    q = qalloc();
X    q->num = z;
X    return q;
X}
X
X
X/*
X * Compute the lcm (least common multiple) of two numbers.
X *    q3 = qlcm(q1, q2);
X */
XNUMBER *
Xqlcm(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER *q;
X
X    if (qiszero(q1) || qiszero(q2))
X        return qlink(&_qzero_);
X    if (q1 == q2)
X        return qabs(q1);
X    if (qisunit(q1))
X        return qabs(q2);
X    if (qisunit(q2))
X        return qabs(q1);
X    q = qalloc();
X    zlcm(q1->num, q2->num, &q->num);
X    if (qisfrac(q1) || qisfrac(q2))
X        zgcd(q1->den, q2->den, &q->den);
X    return q;
X}
X
X
X/*
X * Remove all occurances of the specified factor from a number.
X * Returned number is always positive.
X */
XNUMBER *
Xqfacrem(q1, q2)
X    NUMBER *q1, *q2;
X{
X    long count;
X    ZVALUE tmp;
X    NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integers for factor removal");
X    count = zfacrem(q1->num, q2->num, &tmp);
X    if (zisunit(tmp)) {
X        zfree(tmp);
X        return qlink(&_qone_);
X    }
X    if (count == 0) {
X        zfree(tmp);
X        return qlink(q1);
X    }
X    r = qalloc();
X    r->num = tmp;
X    return r;
X}
X
X
X/*
X * Divide one number by the gcd of it with another number repeatedly until
X * the number is relatively prime.
X */
XNUMBER *
Xqgcdrem(q1, q2)
X    NUMBER *q1, *q2;
X{
X    ZVALUE tmp;
X    NUMBER *r;
X
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integers for gcdrem");
X    zgcdrem(q1->num, q2->num, &tmp);
X    if (zisunit(tmp)) {
X        zfree(tmp);
X        return qlink(&_qone_);
X    }
X    if (zcmp(q1->num, tmp) == 0) {
X        zfree(tmp);
X        return qlink(q1);
X    }
X    r = qalloc();
X    r->num = tmp;
X    return r;
X}
X
X
X/*
X * Return the lowest prime factor of a number.
X * Search is conducted for the specified number of primes.
X * Returns one if no factor was found.
X */
XNUMBER *
Xqlowfactor(q1, q2)
X    NUMBER *q1, *q2;
X{
X    if (qisfrac(q1) || qisfrac(q2))
X        math_error("Non-integers for lowfactor");
X    return itoq(zlowfactor(q1->num, ztoi(q2->num)));
X}
X
X
X/*
X * Return the number of places after the decimal point needed to exactly
X * represent the specified number as a real number.  Integers return zero,
X * and non-terminating decimals return minus one.  Examples:
X *    qplaces(1/7)=-1, qplaces(3/10)= 1, qplaces(1/8)=3, qplaces(4)=0.
X */
Xlong
Xqplaces(q)
X    NUMBER *q;
X{
X    long twopow, fivepow;
X    HALF fiveval[2];
X    ZVALUE five;
X    ZVALUE tmp;
X
X    if (qisint(q))    /* no decimal places if number is integer */
X        return 0;
X    /*
X     * The number of decimal places of a fraction in lowest terms is finite
X     * if an only if the denominator is of the form 2^A * 5^B, and then the
X     * number of decimal places is equal to MAX(A, B).
X     */
X    five.sign = 0;
X    five.len = 1;
X    five.v = fiveval;
X    fiveval[0] = 5;
X    fivepow = zfacrem(q->den, five, &tmp);
X    if (!zisonebit(tmp)) {
X        zfree(tmp);
X        return -1;
X    }
X    twopow = zlowbit(tmp);
X    zfree(tmp);
X    if (twopow < fivepow)
X        twopow = fivepow;
X    return twopow;
X}
X
X
X/*
X * Perform a probabilistic primality test (algorithm P in Knuth).
X * Returns FALSE if definitely not prime, or TRUE if probably prime.
X * Second arg determines how many times to check for primality.
X */
XBOOL
Xqprimetest(q1, q2)
X    NUMBER *q1, *q2;
X{
X    if (qisfrac(q1) || qisfrac(q2) || qisneg(q2))
X        math_error("Bad arguments for qprimetest");
X    return zprimetest(q1->num, qtoi(q2));
X}
X
X
X/*
X * Return a trivial hash value for a number.
X */
XHASH
Xqhash(q)
X    NUMBER *q;
X{
X    HASH hash;
X
X    hash = zhash(q->num);
X    if (qisfrac(q))
X        hash += zhash(q->den) * 2000003;
X    return hash;
X}
X
X/* END CODE */
SHAR_EOF
chmod 0644 calc2.9.0/qfunc.c || echo "restore of calc2.9.0/qfunc.c fails"
set `wc -c calc2.9.0/qfunc.c`;Sum=$1
if test "$Sum" != "24730"
then echo original size 24730, current size $Sum;fi
echo "x - extracting calc2.9.0/qio.c (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/qio.c &&
X/*
X * Copyright (c) 1993 David I. Bell
X * Permission is granted to use, distribute, or modify this source,
X * provided that this copyright notice remains intact.
X *
X * Scanf and printf routines for arbitrary precision rational numbers
X */
X
X#include "stdarg.h"
X#include "qmath.h"
X
X
X#define    PUTCHAR(ch)        math_chr(ch)
X#define    PUTSTR(str)        math_str(str)
X#define    PRINTF1(fmt, a1)    math_fmt(fmt, a1)
X#define    PRINTF2(fmt, a1, a2)    math_fmt(fmt, a1, a2)
X
X
X#if 0
Xstatic long    etoalen;
Xstatic char    *etoabuf = NULL;
X#endif
X
Xstatic long    scalefactor;
Xstatic ZVALUE    scalenumber = { 0, 0, 0 };
X
X
X/*
X * Print a formatted string containing arbitrary numbers, similar to printf.
X * ALL numeric arguments to this routine are rational NUMBERs.
X * Various forms of printing such numbers are supplied, in addition
X * to strings and characters.  Output can actually be to any FILE
X * stream or a string.
X */
X#ifdef VARARGS
X# define VA_ALIST1 fmt, va_alist
X# define VA_DCL1 char *fmt; va_dcl
X#else
X# ifdef __STDC__
X#  define VA_ALIST1 char *fmt, ...
X#  define VA_DCL1
X# else
X#  define VA_ALIST1 fmt
X#  define VA_DCL1 char *fmt;
X# endif
X#endif
X/*VARARGS*/
Xvoid
Xqprintf(VA_ALIST1)
X    VA_DCL1
X{
X    va_list ap;
X    NUMBER *q;
X    int ch, sign;
X    long width, precision;
X
X#ifdef VARARGS
X    va_start(ap);
X#else
X    va_start(ap, fmt);
X#endif
X    while ((ch = *fmt++) != '\0') {
X        if (ch == '\\') {
X            ch = *fmt++;
X            switch (ch) {
X                case 'n': ch = '\n'; break;
X                case 'r': ch = '\r'; break;
X                case 't': ch = '\t'; break;
X                case 'f': ch = '\f'; break;
X                case 'v': ch = '\v'; break;
X                case 'b': ch = '\b'; break;
X                case 0:
X                    va_end(ap);
X                    return;
X            }
X            PUTCHAR(ch);
X            continue;
X        }
X        if (ch != '%') {
X            PUTCHAR(ch);
X            continue;
X        }
X        ch = *fmt++;
X        width = 0; precision = 8; sign = 1;
Xpercent:    ;
X        switch (ch) {
X            case 'd':
X                q = va_arg(ap, NUMBER *);
X                qprintfd(q, width);
X                break;
X            case 'f':
X                q = va_arg(ap, NUMBER *);
X                qprintff(q, width, precision);
X                break;
X            case 'e':
X                q = va_arg(ap, NUMBER *);
X                qprintfe(q, width, precision);
X                break;
X            case 'r':
X            case 'R':
X                q = va_arg(ap, NUMBER *);
X                qprintfr(q, width, (BOOL) (ch == 'R'));
X                break;
X            case 'N':
X                q = va_arg(ap, NUMBER *);
X                zprintval(q->num, 0L, width);
X                break;
X            case 'D':
X                q = va_arg(ap, NUMBER *);
X                zprintval(q->den, 0L, width);
X                break;
X            case 'o':
X                q = va_arg(ap, NUMBER *);
X                qprintfo(q, width);
X                break;
X            case 'x':
X                q = va_arg(ap, NUMBER *);
X                qprintfx(q, width);
X                break;
X            case 'b':
X                q = va_arg(ap, NUMBER *);
X                qprintfb(q, width);
X                break;
X            case 's':
X                PUTSTR(va_arg(ap, char *));
X                break;
X            case 'c':
X                PUTCHAR(va_arg(ap, int));
X                break;
X            case 0:
X                va_end(ap);
X                return;
X            case '-':
X                sign = -1;
X                ch = *fmt++;
X            default:
X        if (('0' <= ch && ch <= '9') || ch == '.' || ch == '*') {
X            if (ch == '*') {
X                q = va_arg(ap, NUMBER *);
X                width = sign * qtoi(q);
X                ch = *fmt++;
X            } else if (ch != '.') {
X                width = ch - '0';
X                while ('0' <= (ch = *fmt++) && ch <= '9')
X                    width = width * 10 + ch - '0';
X                width *= sign;
X            }
X            if (ch == '.') {
X                if ((ch = *fmt++) == '*') {
X                    q = va_arg(ap, NUMBER *);
X                    precision = qtoi(q);
X                    ch = *fmt++;
X                } else {
X                    precision = 0;
X                    while ('0' <= (ch = *fmt++) && ch <= '9')
X                        precision = precision * 10 + ch - '0';
X                }
X            }
X            goto percent;
X        }
X        }
X    }
X    va_end(ap);
X}
X
X
X#if 0
X/*
X * Read a number from the specified FILE stream (NULL means stdin).
X * The number can be an integer, a fraction, a real number, an
X * exponential number, or a hex, octal or binary number.  Leading blanks
X * are skipped.  Illegal numbers return NULL.  Unrecognized characters
X * remain to be read on the line.
X *    q = qreadval(fp);
X */
XNUMBER *
Xqreadval(fp)
X    FILE *fp;        /* file stream to read from (or NULL) */
X{
X    NUMBER *r;        /* returned number */
X    char *cp;         /* current buffer location */
X    long savecc;        /* characters saved in buffer */
X    long scancc;         /* characters parsed correctly */
X    int ch;            /* current character */
X
X    if (fp == NULL)
X        fp = stdin;
X    if (etoabuf == NULL) {
X        etoabuf = (char *)malloc(OUTBUFSIZE + 2);
X        if (etoabuf == NULL)
X            return NULL;
X        etoalen = OUTBUFSIZE;
X    }
X    cp = etoabuf;
X    ch = fgetc(fp);
X    while ((ch == ' ') || (ch == '\t'))
X        ch = fgetc(fp);
X    savecc = 0;
X    for (;;) {
X        if (ch == EOF)
X            return NULL;
X        if (savecc >= etoalen)
X        {
X            cp = (char *)realloc(etoabuf, etoalen + OUTBUFSIZE + 2);
X            if (cp == NULL)
X                return NULL;
X            etoabuf = cp;
X            etoalen += OUTBUFSIZE;
X            cp += savecc;
X        }
X        *cp++ = (char)ch;
X        *cp = '\0';
X        scancc = qparse(etoabuf, QPF_SLASH);
X        if (scancc != ++savecc)
X            break;
X        ch = fgetc(fp);
X    }
X    ungetc(ch, fp);
X    if (scancc < 0)
X        return NULL;
X    r = atoq(etoabuf);
X    if (ziszero(r->den)) {
X        qfree(r);
X        r = NULL;
X    }
X    return r;
X}
X#endif
X
X
X/*
X * Print a number in the specified output mode.
X * If MODE_DEFAULT is given, then the default output mode is used.
X * Any approximate output is flagged with a leading tilde.
X * Integers are always printed as themselves.
X */
Xvoid
Xqprintnum(q, outmode)
X    NUMBER *q;
X{
X    NUMBER tmpval;
X    long prec, exp;
X
X    if (outmode == MODE_DEFAULT)
X        outmode = _outmode_;
X    if ((outmode == MODE_FRAC) || ((outmode == MODE_REAL) && qisint(q))) {
X        qprintfr(q, 0L, FALSE);
X        return;
X    }
X    switch (outmode) {
X        case MODE_INT:
X            if (qisfrac(q))
X                PUTCHAR('~');
X            qprintfd(q, 0L);
X            break;
X
X        case MODE_REAL:
X            prec = qplaces(q);
X            if ((prec < 0) || (prec > _outdigits_)) {
X                prec = _outdigits_;
X                PUTCHAR('~');
X            }
X            qprintff(q, 0L, prec);
X            break;
X
X        case MODE_EXP:
X            if (qiszero(q)) {
X                PUTCHAR('0');
X                return;
X            }
X            tmpval = *q;
X            tmpval.num.sign = 0;
X            exp = qilog10(&tmpval);
X            if (exp == 0) {        /* in range to output as real */
X                qprintnum(q, MODE_REAL);
X                return;
X            }
X            tmpval.num = _one_;
X            tmpval.den = _one_;
X            if (exp > 0)
X                ztenpow(exp, &tmpval.den);
X            else
X                ztenpow(-exp, &tmpval.num);
X            q = qmul(q, &tmpval);
X            zfree(tmpval.num);
X            zfree(tmpval.den);
X            qprintnum(q, MODE_REAL);
X            qfree(q);
X            PRINTF1("e%ld", exp);
X            break;
X
X        case MODE_HEX:
X            qprintfx(q, 0L);
X            break;
X
X        case MODE_OCTAL:
X            qprintfo(q, 0L);
X            break;
X
X        case MODE_BINARY:
X            qprintfb(q, 0L);
X            break;
X
X        default:
X            math_error("Bad mode for print");
X    }
X}
X
X
X/*
X * Print a number in floating point representation.
X * Example:  193.784
X */
Xvoid
Xqprintff(q, width, precision)
X    NUMBER *q;
X    long width;
X    long precision;
X{
X    ZVALUE z, z1;
X
X    if (precision != scalefactor) {
X        if (scalenumber.v)
X            zfree(scalenumber);
X        ztenpow(precision, &scalenumber);
X        scalefactor = precision;
X    }
X    if (scalenumber.v)
X        zmul(q->num, scalenumber, &z);
X    else
X        z = q->num;
X    if (qisfrac(q)) {
X        zquo(z, q->den, &z1);
X        if (z.v != q->num.v)
X            zfree(z);
X        z = z1;
X    }
X    if (qisneg(q) && ziszero(z))
X        PUTCHAR('-');
X    zprintval(z, precision, width);
X    if (z.v != q->num.v)
X        zfree(z);
X}
X
X
X/*
X * Print a number in exponential notation.
X * Example: 4.1856e34
X */
X/*ARGSUSED*/
Xvoid
Xqprintfe(q, width, precision)
X    register NUMBER *q;
X    long width;
X    long precision;
X{
X    long exponent;
X    NUMBER q2;
X    ZVALUE num, den, tenpow, tmp;
X
X    if (qiszero(q)) {
X        PUTSTR("0.0");
X        return;
X    }
X    num = q->num;
X    den = q->den;
X    num.sign = 0;
X    exponent = zdigits(num) - zdigits(den);
X    if (exponent > 0) {
X        ztenpow(exponent, &tenpow);
X        zmul(den, tenpow, &tmp);
X        zfree(tenpow);
X        den = tmp;
X    }
X    if (exponent < 0) {
X        ztenpow(-exponent, &tenpow);
X        zmul(num, tenpow, &tmp);
X        zfree(tenpow);
X        num = tmp;
X    }
X    if (zrel(num, den) < 0) {
X        zmuli(num, 10L, &tmp);
X        if (num.v != q->num.v)
X            zfree(num);
X        num = tmp;
X        exponent--;
X    }
X    q2.num = num;
X    q2.den = den;
X    q2.num.sign = q->num.sign;
X    qprintff(&q2, 0L, precision);
X    if (exponent)
X        PRINTF1("e%ld", exponent);
X    if (num.v != q->num.v)
X        zfree(num);
X    if (den.v != q->den.v)
X        zfree(den);
X}
X
X
X/*
X * Print a number in rational representation.
X * Example: 397/37
X */
Xvoid
Xqprintfr(q, width, force)
X    NUMBER *q;
X    long width;
X    BOOL force;
X{
X    zprintval(q->num, 0L, width);
X    if (force || qisfrac(q)) {
X        PUTCHAR('/');
X        zprintval(q->den, 0L, width);
X    }
X}
X
X
X/*
X * Print a number as an integer (truncating fractional part).
X * Example: 958421
X */
Xvoid
Xqprintfd(q, width)
X    NUMBER *q;
X    long width;
X{
X    ZVALUE z;
X
X    if (qisfrac(q)) {
X        zquo(q->num, q->den, &z);
X        zprintval(z, 0L, width);
X        zfree(z);
X    } else
X        zprintval(q->num, 0L, width);
X}
X
X
X/*
X * Print a number in hex.
X * This prints the numerator and denominator in hex.
X */
Xvoid
Xqprintfx(q, width)
X    NUMBER *q;
X    long width;
X{
X    zprintx(q->num, width);
X    if (qisfrac(q)) {
X        PUTCHAR('/');
X        zprintx(q->den, 0L);
X    }
X}
X
X
X/*
X * Print a number in binary.
X * This prints the numerator and denominator in binary.
X */
Xvoid
Xqprintfb(q, width)
X    NUMBER *q;
X    long width;
X{
X    zprintb(q->num, width);
X    if (qisfrac(q)) {
X        PUTCHAR('/');
X        zprintb(q->den, 0L);
X    }
X}
X
X
X/*
X * Print a number in octal.
X * This prints the numerator and denominator in octal.
X */
Xvoid
Xqprintfo(q, width)
X    NUMBER *q;
X    long width;
X{
X    zprinto(q->num, width);
X    if (qisfrac(q)) {
X        PUTCHAR('/');
X        zprinto(q->den, 0L);
X    }
X}
X
X
X/*
X * Convert a string to a number in rational, floating point,
X * exponential notation, hex, or octal.
X *    q = atoq(string);
X */
XNUMBER *
Xatoq(s)
X    register char *s;
X{
X    register NUMBER *q;
X    register char *t;
X    ZVALUE div, newnum, newden, tmp;
X    long decimals, exp;
X    BOOL hex, negexp;
X
X    q = qalloc();
X    decimals = 0;
X    exp = 0;
X    negexp = FALSE;
X    hex = FALSE;
X    t = s;
X    if ((*t == '+') || (*t == '-'))
X        t++;
X    if ((*t == '0') && ((t[1] == 'x') || (t[1] == 'X'))) {
X        hex = TRUE;
X        t += 2;
X    }
X    while (((*t >= '0') && (*t <= '9')) || (hex &&
X        (((*t >= 'a') && (*t <= 'f')) || ((*t >= 'A') && (*t <= 'F')))))
X            t++;
X    if (*t == '/') {
X        t++;
X        atoz(t, &q->den);
X    } else if ((*t == '.') || (*t == 'e') || (*t == 'E')) {
X        if (*t == '.') {
X            t++;
X            while ((*t >= '0') && (*t <= '9')) {
X                t++;
X                decimals++;
X            }
X        }
X        /*
X         * Parse exponent if any
X         */
X        if ((*t == 'e') || (*t == 'E')) {
X            t++;
X            if (*t == '+')
X                t++;
X            else if (*t == '-') {
X                negexp = TRUE;
X                t++;
X            }
X            while ((*t >= '0') && (*t <= '9')) {
X                exp = (exp * 10) + *t++ - '0';
X                if (exp > 1000000)
X                    math_error("Exponent too large");
X            }
X        }
X        ztenpow(decimals, &q->den);
X    }
X    atoz(s, &q->num);
X    if (qiszero(q)) {
X        qfree(q);
X        return qlink(&_qzero_);
X    }
X    /*
X     * Apply the exponential if any
X     */
X    if (exp) {
X        ztenpow(exp, &tmp);
X        if (negexp) {
X            zmul(q->den, tmp, &newden);
X            zfree(q->den);
X            q->den = newden;
X        } else {
X            zmul(q->num, tmp, &newnum);
X            zfree(q->num);
X            q->num = newnum;
X        }
X        zfree(tmp);
X    }
X    /*
X     * Reduce the fraction to lowest terms
X     */
X    if (zisunit(q->num) || zisunit(q->den))
X        return q;
X    zgcd(q->num, q->den, &div);
X    if (zisunit(div))
X        return q;
X    zquo(q->num, div, &newnum);
X    zfree(q->num);
X    zquo(q->den, div, &newden);
X    zfree(q->den);
X    q->num = newnum;
X    q->den = newden;
X    return q;
X}
X
X
X/*
X * Parse a number in any of the various legal forms, and return the count
X * of characters that are part of a legal number.  Numbers can be either a
X * decimal integer, possibly two decimal integers separated with a slash, a
X * floating point or exponential number, a hex number beginning with "0x",
X * a binary number beginning with "0b", or an octal number beginning with "0".
X * The flags argument modifies the end of number testing for ease in handling
X * fractions or complex numbers.  Minus one is returned if the number format
X * is definitely illegal.
X */
Xlong
Xqparse(cp, flags)
X    register char *cp;
X{
X    char *oldcp;
X
X    oldcp = cp;
X    if ((*cp == '+') || (*cp == '-'))
X        cp++;
X    if ((*cp == '+') || (*cp == '-'))
X        return -1;
X    if ((*cp == '0') && ((cp[1] == 'x') || (cp[1] == 'X'))) {    /* hex */
X        cp += 2;
X        while (((*cp >= '0') && (*cp <= '9')) ||
X            ((*cp >= 'a') && (*cp <= 'f')) ||
X            ((*cp >= 'A') && (*cp <= 'F')))
X                cp++;
X        goto done;
X    }
X    if ((*cp == '0') && ((cp[1] == 'b') || (cp[1] == 'B'))) {    /* binary */
X        cp += 2;
X        while ((*cp == '0') || (*cp == '1'))
X            cp++;
X        goto done;
X    }
X    if ((*cp == '0') && (cp[1] >= '0') && (cp[1] <= '9')) { /* octal */
X        while ((*cp >= '0') && (*cp <= '7'))
X            cp++;
X        goto done;
X    }
X    /*
X     * Number is decimal, but can still be a fraction or real or exponential.
X     */
X    while ((*cp >= '0') && (*cp <= '9'))
X        cp++;
X    if (*cp == '/' && flags & QPF_SLASH) {    /* fraction */
X        cp++;
X        while ((*cp >= '0') && (*cp <= '9'))
X            cp++;
X        goto done;
X    }
X    if (*cp == '.') {    /* floating point */
X        cp++;
X        while ((*cp >= '0') && (*cp <= '9'))
X            cp++;
X    }
X    if ((*cp == 'e') || (*cp == 'E')) {    /* exponential */
X        cp++;
X        if ((*cp == '+') || (*cp == '-'))
X            cp++;
X        if ((*cp == '+') || (*cp == '-'))
X            return -1;
X        while ((*cp >= '0') && (*cp <= '9'))
X            cp++;
X    }
X
Xdone:
X    if (((*cp == 'i') || (*cp == 'I')) && (flags & QPF_IMAG))
X        cp++;
X    if ((*cp == '.') || ((*cp == '/') && (flags & QPF_SLASH)) ||
X        ((*cp >= '0') && (*cp <= '9')) ||
X        ((*cp >= 'a') && (*cp <= 'z')) ||
X        ((*cp >= 'A') && (*cp <= 'Z')))
X            return -1;
X    return (cp - oldcp);
X}
X
X/* END CODE */
SHAR_EOF
chmod 0644 calc2.9.0/qio.c || echo "restore of calc2.9.0/qio.c fails"
set `wc -c calc2.9.0/qio.c`;Sum=$1
if test "$Sum" != "12895"
then echo original size 12895, current size $Sum;fi
echo "x - extracting calc2.9.0/qmath.c (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/qmath.c &&
X/*
X * Copyright (c) 1993 David I. Bell
X * Permission is granted to use, distribute, or modify this source,
X * provided that this copyright notice remains intact.
X *
X * Extended precision rational arithmetic primitive routines
X */
X
X#include "qmath.h"
X
X
XNUMBER _qzero_ =    { { _zeroval_, 1, 0 }, { _oneval_, 1, 0 }, 1 };
XNUMBER _qone_ =        { { _oneval_, 1, 0 }, { _oneval_, 1, 0 }, 1 };
Xstatic NUMBER _qtwo_ =    { { _twoval_, 1, 0 }, { _oneval_, 1, 0 }, 1 };
Xstatic NUMBER _qten_ =    { { _tenval_, 1, 0 }, { _oneval_, 1, 0 }, 1 };
XNUMBER _qnegone_ =    { { _oneval_, 1, 1 }, { _oneval_, 1, 0 }, 1 };
XNUMBER _qonehalf_ =    { { _oneval_, 1, 0 }, { _twoval_, 1, 0 }, 1 };
X
X
X/*
X * Create another copy of a number.
X *    q2 = qcopy(q1);
X */
XNUMBER *
Xqcopy(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    r = qalloc();
X    r->num.sign = q->num.sign;
X    if (!zisunit(q->num)) {
X        r->num.len = q->num.len;
X        r->num.v = alloc(r->num.len);
X        zcopyval(q->num, r->num);
X    }
X    if (!zisunit(q->den)) {
X        r->den.len = q->den.len;
X        r->den.v = alloc(r->den.len);
X        zcopyval(q->den, r->den);
X    }
X    return r;
X}
X
X
X/*
X * Convert a number to a normal integer.
X *    i = qtoi(q);
X */
Xlong
Xqtoi(q)
X    register NUMBER *q;
X{
X    long i;
X    ZVALUE res;
X
X    if (qisint(q))
X        return ztoi(q->num);
X    zquo(q->num, q->den, &res);
X    i = ztoi(res);
X    zfree(res);
X    return i;
X}
X
X
X/*
X * Convert a normal integer into a number.
X *    q = itoq(i);
X */
XNUMBER *
Xitoq(i)
X    long i;
X{
X    register NUMBER *q;
X
X    if ((i >= -1) && (i <= 10)) {
X        switch ((int) i) {
X            case 0: q = &_qzero_; break;
X            case 1: q = &_qone_; break;
X            case 2: q = &_qtwo_; break;
X            case 10: q = &_qten_; break;
X            case -1: q = &_qnegone_; break;
X            default: q = NULL;
X        }
X        if (q)
X            return qlink(q);
X    }
X    q = qalloc();
X    itoz(i, &q->num);
X    return q;
X}
X
X
X/*
X * Create a number from the given integral numerator and denominator.
X *    q = iitoq(inum, iden);
X */
XNUMBER *
Xiitoq(inum, iden)
X    long inum, iden;
X{
X    register NUMBER *q;
X    long d;
X    BOOL sign;
X
X    if (iden == 0)
X        math_error("Division by zero");
X    if (inum == 0)
X        return qlink(&_qzero_);
X    sign = 0;
X    if (inum < 0) {
X        sign = 1;
X        inum = -inum;
X    }
X    if (iden < 0) {
X        sign = 1 - sign;
X        iden = -iden;
X    }
X    d = iigcd(inum, iden);
X    inum /= d;
X    iden /= d;
X    if (iden == 1)
X        return itoq(sign ? -inum : inum);
X    q = qalloc();
X    if (inum != 1)
X        itoz(inum, &q->num);
X    itoz(iden, &q->den);
X    q->num.sign = sign;
X    return q;
X}
X
X
X/*
X * Add two numbers to each other.
X *    q3 = qadd(q1, q2);
X */
XNUMBER *
Xqadd(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER *r;
X    ZVALUE t1, t2, temp, d1, d2, vpd1, upd1;
X
X    if (qiszero(q1))
X        return qlink(q2);
X    if (qiszero(q2))
X        return qlink(q1);
X    r = qalloc();
X    /*
X     * If either number is an integer, then the result is easy.
X     */
X    if (qisint(q1) && qisint(q2)) {
X        zadd(q1->num, q2->num, &r->num);
X        return r;
X    }
X    if (qisint(q2)) {
X        zmul(q1->den, q2->num, &temp);
X        zadd(q1->num, temp, &r->num);
X        zfree(temp);
X        zcopy(q1->den, &r->den);
X        return r;
X    }
X    if (qisint(q1)) {
X        zmul(q2->den, q1->num, &temp);
X        zadd(q2->num, temp, &r->num);
X        zfree(temp);
X        zcopy(q2->den, &r->den);
X        return r;
X    }
X    /*
X     * Both arguments are true fractions, so we need more work.
X     * If the denominators are relatively prime, then the answer is the
X     * straightforward cross product result with no need for reduction.
X     */
X    zgcd(q1->den, q2->den, &d1);
X    if (zisunit(d1)) {
X        zfree(d1);
X        zmul(q1->num, q2->den, &t1);
X        zmul(q1->den, q2->num, &t2);
X        zadd(t1, t2, &r->num);
X        zfree(t1);
X        zfree(t2);
X        zmul(q1->den, q2->den, &r->den);
X        return r;
X    }
X    /*
X     * The calculation is now more complicated.
X     * See Knuth Vol 2 for details.
X     */
X    zquo(q2->den, d1, &vpd1);
X    zquo(q1->den, d1, &upd1);
X    zmul(q1->num, vpd1, &t1);
X    zmul(q2->num, upd1, &t2);
X    zadd(t1, t2, &temp);
X    zfree(t1);
X    zfree(t2);
X    zfree(vpd1);
X    zgcd(temp, d1, &d2);
X    zfree(d1);
X    if (zisunit(d2)) {
X        zfree(d2);
X        r->num = temp;
X        zmul(upd1, q2->den, &r->den);
X        zfree(upd1);
X        return r;
X    }
X    zquo(temp, d2, &r->num);
X    zfree(temp);
X    zquo(q2->den, d2, &temp);
X    zfree(d2);
X    zmul(temp, upd1, &r->den);
X    zfree(temp);
X    zfree(upd1);
X    return r;
X}
X
X
X/*
X * Subtract one number from another.
X *    q3 = qsub(q1, q2);
X */
XNUMBER *
Xqsub(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER t, *r;
X
X    if (q1 == q2)
X        return qlink(&_qzero_);
X    if (qiszero(q2))
X        return qlink(q1);
X    if (qisint(q1) && qisint(q2)) {
X        r = qalloc();
X        zsub(q1->num, q2->num, &r->num);
X        return r;
X    }
X    t = *q2;
X    t.num.sign = !t.num.sign;
X    return qadd(q1, &t);
X}
X
X
X/*
X * Increment a number by one.
X */
XNUMBER *
Xqinc(q)
X    NUMBER *q;
X{
X    NUMBER *r;
X
X    r = qalloc();
X    if (qisint(q)) {
X        zadd(q->num, _one_, &r->num);
X        return r;
X    }
X    zadd(q->num, q->den, &r->num);
X    zcopy(q->den, &r->den);
X    return r;
X}
X
X
X/*
X * Decrement a number by one.
X */
XNUMBER *
Xqdec(q)
X    NUMBER *q;
X{
X    NUMBER *r;
X
X    r = qalloc();
X    if (qisint(q)) {
X        zsub(q->num, _one_, &r->num);
X        return r;
X    }
X    zsub(q->num, q->den, &r->num);
X    zcopy(q->den, &r->den);
X    return r;
X}
X
X
X/*
X * Add a normal small integer value to an arbitrary number.
X */
XNUMBER *
Xqaddi(q1, n)
X    NUMBER *q1;
X    long n;
X{
X    NUMBER addnum;        /* temporary number */
X    HALF addval[2];        /* value of small number */
X    BOOL neg;        /* TRUE if number is neg */
X
X    if (n == 0)
X        return qlink(q1);
X    if (n == 1)
X        return qinc(q1);
X    if (n == -1)
X        return qdec(q1);
X    if (qiszero(q1))
X        return itoq(n);
X    addnum.num.sign = 0;
X    addnum.num.len = 1;
X    addnum.num.v = addval;
X    addnum.den = _one_;
X    neg = (n < 0);
X    if (neg)
X        n = -n;
X    addval[0] = (HALF) n;
X    n = (((FULL) n) >> BASEB);
X    if (n) {
X        addval[1] = (HALF) n;
X        addnum.num.len = 2;
X    }
X    if (neg)
X        return qsub(q1, &addnum);
X    else
X        return qadd(q1, &addnum);
X}
X
X
X/*
X * Multiply two numbers.
X *    q3 = qmul(q1, q2);
X */
XNUMBER *
Xqmul(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER *r;            /* returned value */
X    ZVALUE n1, n2, d1, d2;        /* numerators and denominators */
X    ZVALUE tmp;
X
X    if (qiszero(q1) || qiszero(q2))
X        return qlink(&_qzero_);
X    if (qisone(q1))
X        return qlink(q2);
X    if (qisone(q2))
X        return qlink(q1);
X    if (qisint(q1) && qisint(q2)) {    /* easy results if integers */
X        r = qalloc();
X        zmul(q1->num, q2->num, &r->num);
X        return r;
X    }
X    n1 = q1->num;
X    n2 = q2->num;
X    d1 = q1->den;
X    d2 = q2->den;
X    if (ziszero(d1) || ziszero(d2))
X        math_error("Division by zero");
X    if (ziszero(n1) || ziszero(n2))
X        return qlink(&_qzero_);
X    if (!zisunit(n1) && !zisunit(d2)) {    /* possibly reduce */
X        zgcd(n1, d2, &tmp);
X        if (!zisunit(tmp)) {
X            zquo(q1->num, tmp, &n1);
X            zquo(q2->den, tmp, &d2);
X        }
X        zfree(tmp);
X    }
X    if (!zisunit(n2) && !zisunit(d1)) {    /* again possibly reduce */
X        zgcd(n2, d1, &tmp);
X        if (!zisunit(tmp)) {
X            zquo(q2->num, tmp, &n2);
X            zquo(q1->den, tmp, &d1);
X        }
X        zfree(tmp);
X    }
X    r = qalloc();
X    zmul(n1, n2, &r->num);
X    zmul(d1, d2, &r->den);
X    if (q1->num.v != n1.v)
X        zfree(n1);
X    if (q1->den.v != d1.v)
X        zfree(d1);
X    if (q2->num.v != n2.v)
X        zfree(n2);
X    if (q2->den.v != d2.v)
X        zfree(d2);
X    return r;
X}
X
X
X/*
X * Multiply a number by a small integer.
X *    q2 = qmuli(q1, n);
X */
XNUMBER *
Xqmuli(q, n)
X    NUMBER *q;
X    long n;
X{
X    NUMBER *r;
X    long d;            /* gcd of multiplier and denominator */
X    int sign;
X
X    if ((n == 0) || qiszero(q))
X        return qlink(&_qzero_);
X    if (n == 1)
X        return qlink(q);
X    r = qalloc();
X    if (qisint(q)) {
X        zmuli(q->num, n, &r->num);
X        return r;
X    }
X    sign = 1;
X    if (n < 0) {
X        n = -n;
X        sign = -1;
X    }
X    d = zmodi(q->den, n);
X    d = iigcd(d, n);
X    zmuli(q->num, (n * sign) / d, &r->num);
X    (void) zdivi(q->den, d, &r->den);
X    return r;
X}
X
X
X/*
X * Divide two numbers (as fractions).
X *    q3 = qdiv(q1, q2);
X */
XNUMBER *
Xqdiv(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    NUMBER temp;
X
X    if (qiszero(q2))
X        math_error("Division by zero");
X    if ((q1 == q2) || !qcmp(q1, q2))
X        return qlink(&_qone_);
X    if (qisone(q1))
X        return qinv(q2);
X    temp.num = q2->den;
X    temp.den = q2->num;
X    temp.num.sign = temp.den.sign;
X    temp.den.sign = 0;
X    temp.links = 1;
X    return qmul(q1, &temp);
X}
X
X
X/*
X * Divide a number by a small integer.
X *    q2 = qdivi(q1, n);
X */
XNUMBER *
Xqdivi(q, n)
X    NUMBER *q;
X    long n;
X{
X    NUMBER *r;
X    long d;            /* gcd of divisor and numerator */
X    int sign;
X
X    if (n == 0)
X        math_error("Division by zero");
X    if ((n == 1) || qiszero(q))
X        return qlink(q);
X    sign = 1;
X    if (n < 0) {
X        n = -n;
X        sign = -1;
X    }
X    r = qalloc();
X    d = zmodi(q->num, n);
X    d = iigcd(d, n);
X    (void) zdivi(q->num, d * sign, &r->num);
X    zmuli(q->den, n / d, &r->den);
X    return r;
X}
X
X
X/*
X * Return the quotient when one number is divided by another.
X * This works for fractional values also, and in all cases:
X *    qquo(q1, q2) = int(q1 / q2).
X */
XNUMBER *
Xqquo(q1, q2)
X    register NUMBER *q1, *q2;
X{
X    ZVALUE num, den, res;
X    NUMBER *q;
X
X    if (zisunit(q1->num))
X        num = q2->den;
X    else if (zisunit(q2->den))
X        num = q1->num;
X    else
X        zmul(q1->num, q2->den, &num);
X    if (zisunit(q1->den))
X        den = q2->num;
X    else if (zisunit(q2->num))
X        den = q1->den;
X    else
X        zmul(q1->den, q2->num, &den);
X    zquo(num, den, &res);
X    if ((num.v != q2->den.v) && (num.v != q1->num.v))
X        zfree(num);
X    if ((den.v != q2->num.v) && (den.v != q1->den.v))
X        zfree(den);
X    if (ziszero(res)) {
X        zfree(res);
X        return qlink(&_qzero_);
X    }
X    res.sign = (q1->num.sign != q2->num.sign);
X    if (zisunit(res)) {
X        q = (res.sign ? &_qnegone_ : &_qone_);
X        zfree(res);
X        return qlink(q);
X    }
X    q = qalloc();
X    q->num = res;
X    return q;
X}
X
X
X/*
X * Return the absolute value of a number.
X *    q2 = qabs(q1);
X */
XNUMBER *
Xqabs(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (q->num.sign == 0)
X        return qlink(q);
X    r = qalloc();
X    if (!zisunit(q->num))
X        zcopy(q->num, &r->num);
X    if (!zisunit(q->den))
X        zcopy(q->den, &r->den);
X    r->num.sign = 0;
X    return r;
X}
X
X
X/*
X * Negate a number.
X *    q2 = qneg(q1);
X */
XNUMBER *
Xqneg(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qiszero(q))
X        return qlink(&_qzero_);
X    r = qalloc();
X    if (!zisunit(q->num))
X        zcopy(q->num, &r->num);
X    if (!zisunit(q->den))
X        zcopy(q->den, &r->den);
X    r->num.sign = !q->num.sign;
X    return r;
X}
X
X
X/*
X * Return the sign of a number (-1, 0 or 1)
X */
XNUMBER *
Xqsign(q)
X    NUMBER *q;
X{
X    if (qiszero(q))
X        return qlink(&_qzero_);
X    if (qisneg(q))
X        return qlink(&_qnegone_);
X    return qlink(&_qone_);
X}
X
X
X/*
X * Invert a number.
X *    q2 = qinv(q1);
X */
XNUMBER *
Xqinv(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisunit(q)) {
X        r = (qisneg(q) ? &_qnegone_ : &_qone_);
X        return qlink(r);
X    }
X    if (qiszero(q))
X        math_error("Division by zero");
X    r = qalloc();
X    if (!zisunit(q->num))
X        zcopy(q->num, &r->den);
X    if (!zisunit(q->den))
X        zcopy(q->den, &r->num);
X    r->num.sign = q->num.sign;
X    r->den.sign = 0;
X    return r;
X}
X
X
X/*
X * Return just the numerator of a number.
X *    q2 = qnum(q1);
X */
XNUMBER *
Xqnum(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisint(q))
X        return qlink(q);
X    if (zisunit(q->num)) {
X        r = (qisneg(q) ? &_qnegone_ : &_qone_);
X        return qlink(r);
X    }
X    r = qalloc();
X    zcopy(q->num, &r->num);
X    return r;
X}
X
X
X/*
X * Return just the denominator of a number.
X *    q2 = qden(q1);
X */
XNUMBER *
Xqden(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisint(q))
X        return qlink(&_qone_);
X    r = qalloc();
X    zcopy(q->den, &r->num);
X    return r;
X}
X
X
X/*
X * Return the fractional part of a number.
X *    q2 = qfrac(q1);
X */
XNUMBER *
Xqfrac(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisint(q))
X        return qlink(&_qzero_);
X    if ((q->num.len < q->den.len) || ((q->num.len == q->den.len) &&
X        (q->num.v[q->num.len - 1] < q->den.v[q->num.len - 1])))
X            return qlink(q);
X    r = qalloc();
X    zmod(q->num, q->den, &r->num);
X    zcopy(q->den, &r->den);
X    r->num.sign = q->num.sign;
X    return r;
X}
X
X
X/*
X * Return the integral part of a number.
X *    q2 = qint(q1);
X */
XNUMBER *
Xqint(q)
X    register NUMBER *q;
X{
X    register NUMBER *r;
X
X    if (qisint(q))
X        return qlink(q);
X    if ((q->num.len < q->den.len) || ((q->num.len == q->den.len) &&
X        (q->num.v[q->num.len - 1] < q->den.v[q->num.len - 1])))
SHAR_EOF
echo "End of part 8"
echo "File calc2.9.0/qmath.c is continued in part 9"
echo "9" > s2_seq_.tmp
exit 0