Usenet 1994 January/usenetsourcesnewsgroupsinfomagicjanuary1994.iso/sources/unix/volume27/calc-2.9.0/part13

Text File | 1993-12-07 | 59.0 KB | 2,213 lines

Newsgroups: comp.sources.unix
From: [e-mail] (David I. Bell)
Subject: v27i140: calc-2.9.0 - arbitrary precision C-like programmable calculator, Part13/19
References: <[e-mail]>
Sender: [e-mail]
Approved: [e-mail]

Submitted-By: [e-mail] (David I. Bell)
Posting-Number: Volume 27, Issue 140
Archive-Name: calc-2.9.0/part13

#!/bin/sh
# this is part 13 of a multipart archive
# do not concatenate these parts, unpack them in order with /bin/sh
# file calc2.9.0/zmath.h continued
#
CurArch=13
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/zmath.h"
sed 's/^X//' << 'SHAR_EOF' >> calc2.9.0/zmath.h
X#endif
Xextern void zminmod MATH_PROTO((ZVALUE z1, ZVALUE z2, ZVALUE *res));
Xextern BOOL zcmpmod MATH_PROTO((ZVALUE z1, ZVALUE z2, ZVALUE z3));
X
X
X/*
X * These functions are for internal use only.
X */
Xextern void ztrim MATH_PROTO((ZVALUE *z));
Xextern void zshiftr MATH_PROTO((ZVALUE z, long n));
Xextern void zshiftl MATH_PROTO((ZVALUE z, long n));
Xextern HALF *zalloctemp MATH_PROTO((LEN len));
Xextern void initmasks MATH_PROTO((void));
X
X
X/*
X * Modulo arithmetic definitions.
X * Structure holding state of REDC initialization.
X * Multiple instances of this structure can be used allowing
X * calculations with more than one modulus at the same time.
X * Len of zero means the structure is not initialized.
X */
Xtypedef    struct {
X    LEN len;        /* number of words in binary modulus */
X    ZVALUE mod;        /* modulus REDC is computing with */
X    ZVALUE inv;        /* inverse of modulus in binary modulus */
X    ZVALUE one;        /* REDC format for the number 1 */
X} REDC;
X
Xextern REDC *zredcalloc MATH_PROTO((ZVALUE z1));
Xextern void zredcfree MATH_PROTO((REDC *rp));
Xextern void zredcencode MATH_PROTO((REDC *rp, ZVALUE z1, ZVALUE *res));
Xextern void zredcdecode MATH_PROTO((REDC *rp, ZVALUE z1, ZVALUE *res));
Xextern void zredcmul MATH_PROTO((REDC *rp, ZVALUE z1, ZVALUE z2, ZVALUE *res));
Xextern void zredcsquare MATH_PROTO((REDC *rp, ZVALUE z1, ZVALUE *res));
Xextern void zredcpower MATH_PROTO((REDC *rp, ZVALUE z1, ZVALUE z2, ZVALUE *res));
X
X
X/*
X * macro expansions to speed this thing up
X */
X#define ziseven(z)    (!(*(z).v & 01))
X#define zisodd(z)    (*(z).v & 01)
X#define ziszero(z)    ((*(z).v == 0) && ((z).len == 1))
X#define zisneg(z)    ((z).sign)
X#define zispos(z)    (((z).sign == 0) && (*(z).v || ((z).len > 1)))
X#define zisunit(z)    ((*(z).v == 1) && ((z).len == 1))
X#define zisone(z)    ((*(z).v == 1) && ((z).len == 1) && !(z).sign)
X#define zisnegone(z)    ((*(z).v == 1) && ((z).len == 1) && (z).sign)
X#define zistwo(z)    ((*(z).v == 2) && ((z).len == 1) && !(z).sign)
X#define zisleone(z)    ((*(z).v <= 1) && ((z).len == 1))
X#define zistiny(z)    ((z).len == 1)
X#define zissmall(z)    (((z).len < 2) || (((z).len == 2) && (((short)(z).v[1]) >= 0)))
X#define zisbig(z)    (((z).len > 2) || (((z).len == 2) && (((short)(z).v[1]) < 0)))
X
X#define z1tol(z)    ((long)((z).v[0]))
X#define z2tol(z)    (((long)((z).v[0])) + \
X                (((long)((z).v[1] & MAXHALF)) << BASEB))
X#define    zclearval(z)    memset((z).v, 0, (z).len * sizeof(HALF))
X#define    zcopyval(z1,z2)    memcpy((z2).v, (z1).v, (z1).len * sizeof(HALF))
X#define zquicktrim(z)    {if (((z).len > 1) && ((z).v[(z).len-1] == 0)) \
X                (z).len--;}
X#define    zfree(z)    freeh((z).v)
X
X
X/*
X * Output modes for numeric displays.
X */
X#define MODE_DEFAULT    0
X#define MODE_FRAC    1
X#define MODE_INT    2
X#define MODE_REAL    3
X#define MODE_EXP    4
X#define MODE_HEX    5
X#define MODE_OCTAL    6
X#define MODE_BINARY    7
X#define MODE_MAX    7
X
X#define MODE_INITIAL    MODE_REAL
X
X
X/*
X * Output routines for either FILE handles or strings.
X */
Xextern void math_chr MATH_PROTO((int ch));
Xextern void math_str MATH_PROTO((char *str));
Xextern void math_fill MATH_PROTO((char *str, long width));
Xextern void math_flush MATH_PROTO((void));
Xextern void math_divertio MATH_PROTO((void));
Xextern void math_cleardiversions MATH_PROTO((void));
Xextern void math_setfp MATH_PROTO((FILE *fp));
Xextern char *math_getdivertedio MATH_PROTO((void));
Xextern int math_setmode MATH_PROTO((int mode));
Xextern long math_setdigits MATH_PROTO((long digits));
X
X
X#ifdef VARARGS
Xextern void math_fmt();
X#else
Xextern void math_fmt MATH_PROTO((char *, ...));
X#endif
X
X
X/*
X * The error routine.
X */
X#ifdef VARARGS
Xextern void math_error();
X#else
Xextern void math_error MATH_PROTO((char *, ...));
X#endif
X
X
X/*
X * constants used often by the arithmetic routines
X */
Xextern HALF _zeroval_[], _oneval_[], _twoval_[], _tenval_[];
Xextern ZVALUE _zero_, _one_, _ten_;
X
Xextern BOOL _math_abort_;    /* nonzero to abort calculations */
Xextern ZVALUE _tenpowers_[32];    /* table of 10^2^n */
Xextern int _outmode_;        /* current output mode */
Xextern LEN _mul2_;        /* size of number to use multiply algorithm 2 */
Xextern LEN _sq2_;        /* size of number to use square algorithm 2 */
Xextern LEN _pow2_;        /* size of modulus to use REDC for powers */
Xextern LEN _redc2_;        /* size of modulus to use REDC algorithm 2 */
Xextern HALF *bitmask;        /* bit rotation, norm 0 */
X
X#endif
X
X/* END CODE */
SHAR_EOF
echo "File calc2.9.0/zmath.h is complete"
chmod 0644 calc2.9.0/zmath.h || echo "restore of calc2.9.0/zmath.h fails"
set `wc -c calc2.9.0/zmath.h`;Sum=$1
if test "$Sum" != "11814"
then echo original size 11814, current size $Sum;fi
echo "x - extracting calc2.9.0/zmod.c (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/zmod.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 * Routines to do modulo arithmetic both normally and also using the REDC
X * algorithm given by Peter L. Montgomery in Mathematics of Computation,
X * volume 44, number 170 (April, 1985).  For multiple multiplies using
X * the same large modulus, the REDC algorithm avoids the usual division
X * by the modulus, instead replacing it with two multiplies or else a
X * special algorithm.  When these two multiplies or the special algorithm
X * are faster then the division, then the REDC algorithm is better.
X */
X
X#include "zmath.h"
X
X
X#define    POWBITS    4        /* bits for power chunks (must divide BASEB) */
X#define    POWNUMS    (1<<POWBITS)    /* number of powers needed in table */
X
X
XLEN _pow2_ = POW_ALG2;        /* modulo size to use REDC for powers */
XLEN _redc2_ = REDC_ALG2;    /* modulo size to use second REDC algorithm */
X
Xstatic REDC *powermodredc = NULL;    /* REDC info for raising to power */
X
X#if 0
Xextern void zaddmod MATH_PROTO((ZVALUE z1, ZVALUE z2, ZVALUE z3, ZVALUE *res));
Xextern void znegmod MATH_PROTO((ZVALUE z1, ZVALUE z2, ZVALUE *res));
X
X/*
X * Multiply two numbers together and then mod the result with a third number.
X * The two numbers to be multiplied can be negative or out of modulo range.
X * The result will be in the range 0 to the modulus - 1.
X */
Xvoid
Xzmulmod(z1, z2, z3, res)
X    ZVALUE z1;        /* first number to be multiplied */
X    ZVALUE z2;        /* second number to be multiplied */
X    ZVALUE z3;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    ZVALUE tmp;
X    FULL prod;
X    FULL digit;
X    BOOL neg;
X
X    if (ziszero(z3) || zisneg(z3))
X        math_error("Mod of non-positive integer");
X    if (ziszero(z1) || ziszero(z2) || zisunit(z3)) {
X        *res = _zero_;
X        return;
X    }
X
X    /*
X     * If the modulus is a single digit number, then do the result
X     * cheaply.  Check especially for a small power of two.
X     */
X    if (zistiny(z3)) {
X        neg = (z1.sign != z2.sign);
X        digit = z3.v[0];
X        if ((digit & -digit) == digit) {    /* NEEDS 2'S COMP */
X            prod = ((FULL) z1.v[0]) * ((FULL) z2.v[0]);
X            prod &= (digit - 1);
X        } else {
X            z1.sign = 0;
X            z2.sign = 0;
X            prod = (FULL) zmodi(z1, (long) digit);
X            prod *= (FULL) zmodi(z2, (long) digit);
X            prod %= digit;
X        }
X        if (neg && prod)
X            prod = digit - prod;
X        itoz((long) prod, res);
X        return;
X    }
X
X    /*
X     * The modulus is more than one digit.
X     * Actually do the multiply and divide if necessary.
X     */
X    zmul(z1, z2, &tmp);
X    if (zispos(tmp) && ((tmp.len < z3.len) || ((tmp.len == z3.len) &&
X        (tmp.v[tmp.len-1] < z2.v[z3.len-1]))))
X    {
X        *res = tmp;
X        return;
X    }
X    zmod(tmp, z3, res);
X    zfree(tmp);
X}
X
X
X/*
X * Square a number and then mod the result with a second number.
X * The number to be squared can be negative or out of modulo range.
X * The result will be in the range 0 to the modulus - 1.
X */
Xvoid
Xzsquaremod(z1, z2, res)
X    ZVALUE z1;        /* number to be squared */
X    ZVALUE z2;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    ZVALUE tmp;
X    FULL prod;
X    FULL digit;
X
X    if (ziszero(z2) || zisneg(z2))
X        math_error("Mod of non-positive integer");
X    if (ziszero(z1) || zisunit(z2)) {
X        *res = _zero_;
X        return;
X    }
X
X    /*
X     * If the modulus is a single digit number, then do the result
X     * cheaply.  Check especially for a small power of two.
X     */
X    if (zistiny(z2)) {
X        digit = z2.v[0];
X        if ((digit & -digit) == digit) {    /* NEEDS 2'S COMP */
X            prod = (FULL) z1.v[0];
X            prod = (prod * prod) & (digit - 1);
X        } else {
X            z1.sign = 0;
X            prod = (FULL) zmodi(z1, (long) digit);
X            prod = (prod * prod) % digit;
X        }
X        itoz((long) prod, res);
X        return;
X    }
X
X    /*
X     * The modulus is more than one digit.
X     * Actually do the square and divide if necessary.
X     */
X    zsquare(z1, &tmp);
X    if ((tmp.len < z2.len) ||
X        ((tmp.len == z2.len) && (tmp.v[tmp.len-1] < z2.v[z2.len-1]))) {
X            *res = tmp;
X            return;
X    }
X    zmod(tmp, z2, res);
X    zfree(tmp);
X}
X
X
X/*
X * Add two numbers together and then mod the result with a third number.
X * The two numbers to be added can be negative or out of modulo range.
X * The result will be in the range 0 to the modulus - 1.
X */
Xstatic void
Xzaddmod(z1, z2, z3, res)
X    ZVALUE z1;        /* first number to be added */
X    ZVALUE z2;        /* second number to be added */
X    ZVALUE z3;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    ZVALUE tmp;
X    FULL sumdigit;
X    FULL moddigit;
X
X    if (ziszero(z3) || zisneg(z3))
X        math_error("Mod of non-positive integer");
X    if ((ziszero(z1) && ziszero(z2)) || zisunit(z3)) {
X        *res = _zero_;
X        return;
X    }
X    if (zistwo(z2)) {
X        if ((z1.v[0] + z2.v[0]) & 0x1)
X            *res = _one_;
X        else
X            *res = _zero_;
X        return;
X    }
X    zadd(z1, z2, &tmp);
X    if (zisneg(tmp) || (tmp.len > z3.len)) {
X        zmod(tmp, z3, res);
X        zfree(tmp);
X        return;
X    }
X    sumdigit = tmp.v[tmp.len - 1];
X    moddigit = z3.v[z3.len - 1];
X    if ((tmp.len < z3.len) || (sumdigit < moddigit)) {
X        *res = tmp;
X        return;
X    }
X    if (sumdigit < 2 * moddigit) {
X        zsub(tmp, z3, res);
X        zfree(tmp);
X        return;
X    }
X    zmod(tmp, z2, res);
X    zfree(tmp);
X}
X
X
X/*
X * Subtract two numbers together and then mod the result with a third number.
X * The two numbers to be subtract can be negative or out of modulo range.
X * The result will be in the range 0 to the modulus - 1.
X */
Xvoid
Xzsubmod(z1, z2, z3, res)
X    ZVALUE z1;        /* number to be subtracted from */
X    ZVALUE z2;        /* number to be subtracted */
X    ZVALUE z3;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    if (ziszero(z3) || zisneg(z3))
X        math_error("Mod of non-positive integer");
X    if (ziszero(z2)) {
X        zmod(z1, z3, res);
X        return;
X    }
X    if (ziszero(z1)) {
X        znegmod(z2, z3, res);
X        return;
X    }
X    if ((z1.sign == z2.sign) && (z1.len == z2.len) &&
X        (z1.v[0] == z2.v[0]) && (zcmp(z1, z2) == 0)) {
X            *res = _zero_;
X            return;
X    }
X    z2.sign = !z2.sign;
X    zaddmod(z1, z2, z3, res);
X}
X
X
X/*
X * Calculate the negative of a number modulo another number.
X * The number to be negated can be negative or out of modulo range.
X * The result will be in the range 0 to the modulus - 1.
X */
Xstatic void
Xznegmod(z1, z2, res)
X    ZVALUE z1;        /* number to take negative of */
X    ZVALUE z2;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    int sign;
X    int cv;
X
X    if (ziszero(z2) || zisneg(z2))
X        math_error("Mod of non-positive integer");
X    if (ziszero(z1) || zisunit(z2)) {
X        *res = _zero_;
X        return;
X    }
X    if (zistwo(z2)) {
X        if (z1.v[0] & 0x1)
X            *res = _one_;
X        else
X            *res = _zero_;
X        return;
X    }
X
X    /*
X     * If the absolute value of the number is within the modulo range,
X     * then the result is just a copy or a subtraction.  Otherwise go
X     * ahead and negate and reduce the result.
X     */
X    sign = z1.sign;
X    z1.sign = 0;
X    cv = zrel(z1, z2);
X    if (cv == 0) {
X        *res = _zero_;
X        return;
X    }
X    if (cv < 0) {
X        if (sign)
X            zcopy(z1, res);
X        else
X            zsub(z2, z1, res);
X        return;
X    }
X    z1.sign = !sign;
X    zmod(z1, z2, res);
X}
X#endif
X
X
X/*
X * Calculate the number congruent to the given number whose absolute
X * value is minimal.  The number to be reduced can be negative or out of
X * modulo range.  The result will be within the range -int((modulus-1)/2)
X * to int(modulus/2) inclusive.  For example, for modulus 7, numbers are
X * reduced to the range [-3, 3], and for modulus 8, numbers are reduced to
X * the range [-3, 4].
X */
Xvoid
Xzminmod(z1, z2, res)
X    ZVALUE z1;        /* number to find minimum congruence of */
X    ZVALUE z2;        /* number to take mod with */
X    ZVALUE *res;        /* result */
X{
X    ZVALUE tmp1, tmp2;
X    int sign;
X    int cv;
X
X    if (ziszero(z2) || zisneg(z2))
X        math_error("Mod of non-positive integer");
X    if (ziszero(z1) || zisunit(z2)) {
X        *res = _zero_;
X        return;
X    }
X    if (zistwo(z2)) {
X        if (zisodd(z1))
X            *res = _one_;
X        else
X            *res = _zero_;
X        return;
X    }
X
X    /*
X     * Do a quick check to see if the number is very small compared
X     * to the modulus.  If so, then the result is obvious.
X     */
X    if (z1.len < z2.len - 1) {
X        zcopy(z1, res);
X        return;
X    }
X
X    /*
X     * Now make sure the input number is within the modulo range.
X     * If not, then reduce it to be within range and make the
X     * quick check again.
X     */
X    sign = z1.sign;
X    z1.sign = 0;
X    cv = zrel(z1, z2);
X    if (cv == 0) {
X        *res = _zero_;
X        return;
X    }
X    tmp1 = z1;
X    if (cv > 0) {
X        z1.sign = (BOOL)sign;
X        zmod(z1, z2, &tmp1);
X        if (tmp1.len < z2.len - 1) {
X            *res = tmp1;
X            return;
X        }
X        sign = 0;
X    }
X
X    /*
X     * Now calculate the difference of the modulus and the absolute
X     * value of the original number.  Compare the original number with
X     * the difference, and return the one with the smallest absolute
X     * value, with the correct sign.  If the two values are equal, then
X     * return the positive result.
X     */
X    zsub(z2, tmp1, &tmp2);
X    cv = zrel(tmp1, tmp2);
X    if (cv < 0) {
X        zfree(tmp2);
X        tmp1.sign = (BOOL)sign;
X        if (tmp1.v == z1.v)
X            zcopy(tmp1, res);
X        else
X            *res = tmp1;
X    } else {
X        if (cv)
X            tmp2.sign = !sign;
X        if (tmp1.v != z1.v)
X            zfree(tmp1);
X        *res = tmp2;
X    }
X}
X
X
X/*
X * Compare two numbers for equality modulo a third number.
X * The two numbers to be compared can be negative or out of modulo range.
X * Returns TRUE if the numbers are not congruent, and FALSE if they are
X * congruent.
X */
XBOOL
Xzcmpmod(z1, z2, z3)
X    ZVALUE z1;        /* first number to be compared */
X    ZVALUE z2;        /* second number to be compared */
X    ZVALUE z3;        /* modulus */
X{
X    ZVALUE tmp1, tmp2, tmp3;
X    FULL digit;
X    LEN len;
X    int cv;
X
X    if (zisneg(z3) || ziszero(z3))
X        math_error("Non-positive modulus in zcmpmod");
X    if (zistwo(z3))
X        return (((z1.v[0] + z2.v[0]) & 0x1) != 0);
X
X    /*
X     * If the two numbers are equal, then their mods are equal.
X     */
X    if ((z1.sign == z2.sign) && (z1.len == z2.len) &&
X        (z1.v[0] == z2.v[0]) && (zcmp(z1, z2) == 0))
X            return FALSE;
X
X    /*
X     * If both numbers are negative, then we can make them positive.
X     */
X    if (zisneg(z1) && zisneg(z2)) {
X        z1.sign = 0;
X        z2.sign = 0;
X    }
X
X    /*
X     * For small negative numbers, make them positive before comparing.
X     * In any case, the resulting numbers are in tmp1 and tmp2.
X     */
X    tmp1 = z1;
X    tmp2 = z2;
X    len = z3.len;
X    digit = z3.v[len - 1];
X
X    if (zisneg(z1) && ((z1.len < len) ||
X        ((z1.len == len) && (z1.v[z1.len - 1] < digit))))
X            zadd(z1, z3, &tmp1);
X
X    if (zisneg(z2) && ((z2.len < len) ||
X        ((z2.len == len) && (z2.v[z2.len - 1] < digit))))
X            zadd(z2, z3, &tmp2);
X
X    /*
X     * Now compare the two numbers for equality.
X     * If they are equal we are all done.
X     */
X    if (zcmp(tmp1, tmp2) == 0) {
X        if (tmp1.v != z1.v)
X            zfree(tmp1);
X        if (tmp2.v != z2.v)
X            zfree(tmp2);
X        return FALSE;
X    }
X
X    /*
X     * They are not identical.  Now if both numbers are positive
X     * and less than the modulus, then they are definitely not equal.
X     */
X    if ((tmp1.sign == tmp2.sign) &&
X        ((tmp1.len < len) || (zrel(tmp1, z3) < 0)) &&
X        ((tmp2.len < len) || (zrel(tmp2, z3) < 0)))
X    {
X        if (tmp1.v != z1.v)
X            zfree(tmp1);
X        if (tmp2.v != z2.v)
X            zfree(tmp2);
X        return TRUE;
X    }
X
X    /*
X     * Either one of the numbers is negative or is large.
X     * So do the standard thing and subtract the two numbers.
X     * Then they are equal if the result is 0 (mod z3).
X     */
X    zsub(tmp1, tmp2, &tmp3);
X    if (tmp1.v != z1.v)
X        zfree(tmp1);
X    if (tmp2.v != z2.v)
X        zfree(tmp2);
X
X    /*
X     * Compare the result with the modulus to see if it is equal to
X     * or less than the modulus.  If so, we know the mod result.
X     */
X    tmp3.sign = 0;
X    cv = zrel(tmp3, z3);
X    if (cv == 0) {
X        zfree(tmp3);
X        return FALSE;
X    }
X    if (cv < 0) {
X        zfree(tmp3);
X        return TRUE;
X    }
X
X    /*
X     * We are forced to actually do the division.
X     * The numbers are congruent if the result is zero.
X     */
X    zmod(tmp3, z3, &tmp1);
X    zfree(tmp3);
X    if (ziszero(tmp1)) {
X        zfree(tmp1);
X        return FALSE;
X    } else {
X        zfree(tmp1);
X        return TRUE;
X    }
X}
X
X
X/*
X * Compute the result of raising one number to a power modulo another number.
X * That is, this computes:  a^b (modulo c).
X * This calculates the result by examining the power POWBITS bits at a time,
X * using a small table of POWNUMS low powers to calculate powers for those bits,
X * and repeated squaring and multiplying by the partial powers to generate
X * the complete power.  If the power being raised to is high enough, then
X * this uses the REDC algorithm to avoid doing many divisions.  When using
X * REDC, multiple calls to this routine using the same modulus will be
X * slightly faster.
X */
Xvoid
Xzpowermod(z1, z2, z3, res)
X    ZVALUE z1, z2, z3, *res;
X{
X    HALF *hp;        /* pointer to current word of the power */
X    REDC *rp;        /* REDC information to be used */
X    ZVALUE *pp;        /* pointer to low power table */
X    ZVALUE ans, temp;    /* calculation values */
X    ZVALUE modpow;        /* current small power */
X    ZVALUE lowpowers[POWNUMS];    /* low powers */
X    int sign;        /* original sign of number */
X    int curshift;        /* shift value for word of power */
X    HALF curhalf;        /* current word of power */
X    unsigned int curpow;    /* current low power */
X    unsigned int curbit;    /* current bit of low power */
X    int i;
X
X    if (zisneg(z3) || ziszero(z3))
X        math_error("Non-positive modulus in zpowermod");
X    if (zisneg(z2))
X        math_error("Negative power in zpowermod");
X
X    sign = z1.sign;
X    z1.sign = 0;
X
X    /*
X     * Check easy cases first.
X     */
X    if (ziszero(z1) || zisunit(z3)) {    /* 0^x or mod 1 */
X        *res = _zero_;
X        return;
X    }
X    if (zistwo(z3)) {            /* mod 2 */
X        if (zisodd(z1))
X            *res = _one_;
X        else
X            *res = _zero_;
X        return;
X    }
X    if (zisunit(z1) && (!sign || ziseven(z2))) {
X        /* 1^x or (-1)^(2x) */
X        *res = _one_;
X        return;
X    }
X
X    /*
X     * Normalize the number being raised to be non-negative and to lie
X     * within the modulo range.  Then check for zero or one specially.
X     */
X    zmod(z1, z3, &temp);
X    if (ziszero(temp)) {
X        zfree(temp);
X        *res = _zero_;
X        return;
X    }
X    z1 = temp;
X    if (sign) {
X        zsub(z3, z1, &temp);
X        zfree(z1);
X        z1 = temp;
X    }
X    if (zisunit(z1)) {
X        zfree(z1);
X        *res = _one_;
X        return;
X    }
X
X    /*
X     * If the modulus is odd, large enough, is not one less than an
X     * exact power of two, and if the power is large enough, then use
X     * the REDC algorithm.  The size where this is done is configurable.
X     */
X    if ((z2.len > 1) && (z3.len >= _pow2_) && zisodd(z3)
X        && !zisallbits(z3))
X    {
X        if (powermodredc && zcmp(powermodredc->mod, z3)) {
X            zredcfree(powermodredc);
X            powermodredc = NULL;
X        }
X        if (powermodredc == NULL)
X            powermodredc = zredcalloc(z3);
X        rp = powermodredc;
X        zredcencode(rp, z1, &temp);
X        zredcpower(rp, temp, z2, &z1);
X        zfree(temp);
X        zredcdecode(rp, z1, res);
X        zfree(z1);
X        return;
X    }
X
X    /*
X     * Modulus or power is small enough to perform the power raising
X     * directly.  Initialize the table of powers.
X     */
X    for (pp = &lowpowers[2]; pp < &lowpowers[POWNUMS]; pp++)
X        pp->len = 0;
X    lowpowers[0] = _one_;
X    lowpowers[1] = z1;
X    ans = _one_;
X
X    hp = &z2.v[z2.len - 1];
X    curhalf = *hp;
X    curshift = BASEB - POWBITS;
X    while (curshift && ((curhalf >> curshift) == 0))
X        curshift -= POWBITS;
X
X    /*
X     * Calculate the result by examining the power POWBITS bits at a time,
X     * and use the table of low powers at each iteration.
X     */
X    for (;;) {
X        curpow = (curhalf >> curshift) & (POWNUMS - 1);
X        pp = &lowpowers[curpow];
X
X        /*
X         * If the small power is not yet saved in the table, then
X         * calculate it and remember it in the table for future use.
X         */
X        if (pp->len == 0) {
X            if (curpow & 0x1)
X                zcopy(z1, &modpow);
X            else
X                modpow = _one_;
X
X            for (curbit = 0x2; curbit <= curpow; curbit *= 2) {
X                pp = &lowpowers[curbit];
X                if (pp->len == 0) {
X                    zsquare(lowpowers[curbit/2], &temp);
X                    zmod(temp, z3, pp);
X                    zfree(temp);
X                }
X                if (curbit & curpow) {
X                    zmul(*pp, modpow, &temp);
X                    zfree(modpow);
X                    zmod(temp, z3, &modpow);
X                    zfree(temp);
X                }
X            }
X            pp = &lowpowers[curpow];
X            *pp = modpow;
X        }
X
X        /*
X         * If the power is nonzero, then accumulate the small power
X         * into the result.
X         */
X        if (curpow) {
X            zmul(ans, *pp, &temp);
X            zfree(ans);
X            zmod(temp, z3, &ans);
X            zfree(temp);
X        }
X
X        /*
X         * Select the next POWBITS bits of the power, if there is
X         * any more to generate.
X         */
X        curshift -= POWBITS;
X        if (curshift < 0) {
X            if (hp-- == z2.v)
X                break;
X            curhalf = *hp;
X            curshift = BASEB - POWBITS;
X        }
X
X        /*
X         * Square the result POWBITS times to make room for the next
X         * chunk of bits.
X         */
X        for (i = 0; i < POWBITS; i++) {
X            zsquare(ans, &temp);
X            zfree(ans);
X            zmod(temp, z3, &ans);
X            zfree(temp);
X        }
X    }
X
X    for (pp = &lowpowers[2]; pp < &lowpowers[POWNUMS]; pp++) {
X        if (pp->len)
X            freeh(pp->v);
X    }
X    *res = ans;
X}
X
X
X/*
X * Initialize the REDC algorithm for a particular modulus,
X * returning a pointer to a structure that is used for other
X * REDC calls.  An error is generated if the structure cannot
X * be allocated.  The modulus must be odd and positive.
X */
XREDC *
Xzredcalloc(z1)
X    ZVALUE z1;        /* modulus to initialize for */
X{
X    REDC *rp;        /* REDC information */
X    ZVALUE tmp;
X    long bit;
X
X    if (ziseven(z1) || zisneg(z1))
X        math_error("REDC requires positive odd modulus");
X
X    rp = (REDC *) malloc(sizeof(REDC));
X    if (rp == NULL)
X        math_error("Cannot allocate REDC structure");
X
X    /*
X     * Round up the binary modulus to the next power of two
X     * which is at a word boundary.  Then the shift and modulo
X     * operations mod the binary modulus can be done very cheaply.
X     * Calculate the REDC format for the number 1 for future use.
X     */
X    bit = zhighbit(z1) + 1;
X    if (bit % BASEB)
X        bit += (BASEB - (bit % BASEB));
X    zcopy(z1, &rp->mod);
X    zbitvalue(bit, &tmp);
X    z1.sign = 1;
X    (void) zmodinv(z1, tmp, &rp->inv);
X    zmod(tmp, rp->mod, &rp->one);
X    zfree(tmp);
X    rp->len = bit / BASEB;
X    return rp;
X}
X
X
X/*
X * Free any numbers associated with the specified REDC structure,
X * and then the REDC structure itself.
X */
Xvoid
Xzredcfree(rp)
X    REDC *rp;        /* REDC information to be cleared */
X{
X    zfree(rp->mod);
X    zfree(rp->inv);
X    zfree(rp->one);
X    free(rp);
X}
X
X
X/*
X * Convert a normal number into the specified REDC format.
X * The number to be converted can be negative or out of modulo range.
X * The resulting number can be used for multiplying, adding, subtracting,
X * or comparing with any other such converted numbers, as if the numbers
X * were being calculated modulo the number which initialized the REDC
X * information.  When the final value is unconverted, the result is the
X * same as if the usual operations were done with the original numbers.
X */
Xvoid
Xzredcencode(rp, z1, res)
X    REDC *rp;        /* REDC information */
X    ZVALUE z1;        /* number to be converted */
X    ZVALUE *res;        /* returned converted number */
X{
X    ZVALUE tmp1, tmp2;
X
X    /*
X     * Handle the cases 0, 1, -1, and 2 specially since these are
X     * easy to calculate.  Zero transforms to zero, and the others
X     * can be obtained from the precomputed REDC format for 1 since
X     * addition and subtraction act normally for REDC format numbers.
X     */
X    if (ziszero(z1)) {
X        *res = _zero_;
X        return;
X    }
X    if (zisone(z1)) {
X        zcopy(rp->one, res);
X        return;
X    }
X    if (zisunit(z1)) {
X        zsub(rp->mod, rp->one, res);
X        return;
X    }
X    if (zistwo(z1)) {
X        zadd(rp->one, rp->one, &tmp1);
X        if (zrel(tmp1, rp->mod) < 0) {
X            *res = tmp1;
X            return;
X        }
X        zsub(tmp1, rp->mod, res);
X        zfree(tmp1);
X        return;
X    }
X
X    /*
X     * Not a trivial number to convert, so do the full transformation.
X     * Convert negative numbers to positive numbers before converting.
X     */
X    tmp1.len = 0;
X    if (zisneg(z1)) {
X        zmod(z1, rp->mod, &tmp1);
X        z1 = tmp1;
X    }
X    zshift(z1, rp->len * BASEB, &tmp2);
X    if (tmp1.len)
X        zfree(tmp1);
X    zmod(tmp2, rp->mod, res);
X    zfree(tmp2);
X}
X
X
X/*
X * The REDC algorithm used to convert numbers out of REDC format and also
X * used after multiplication of two REDC numbers.  Using this routine
X * avoids any divides, replacing the divide by two multiplications.
X * If the numbers are very large, then these two multiplies will be
X * quicker than the divide, since dividing is harder than multiplying.
X */
Xvoid
Xzredcdecode(rp, z1, res)
X    REDC *rp;        /* REDC information */
X    ZVALUE z1;        /* number to be transformed */
X    ZVALUE *res;        /* returned transformed number */
X{
X    ZVALUE tmp1, tmp2;    /* temporaries */
X    HALF *hp;        /* saved pointer to tmp2 value */
X
X    if (zisneg(z1))
X        math_error("Negative number for zredc");
X
X    /*
X     * Check first for the special values for 0 and 1 that are easy.
X     */
X    if (ziszero(z1)) {
X        *res = _zero_;
X        return;
X    }
X    if ((z1.len == rp->one.len) && (z1.v[0] == rp->one.v[0]) &&
X        (zcmp(z1, rp->one) == 0)) {
X            *res = _one_;
X            return;
X    }
X
X    /*
X     * First calculate the following:
X     *     tmp2 = ((z1 % 2^bitnum) * inv) % 2^bitnum.
X     * The mod operations can be done with no work since the bit
X     * number was selected as a multiple of the word size.  Just
X     * reduce the sizes of the numbers as required.
X     */
X    tmp1 = z1;
X    if (tmp1.len > rp->len)
X        tmp1.len = rp->len;
X    zmul(tmp1, rp->inv, &tmp2);
X    if (tmp2.len > rp->len)
X        tmp2.len = rp->len;
X
X    /*
X     * Next calculate the following:
X     *    res = (z1 + tmp2 * modulus) / 2^bitnum
X     * The division by a power of 2 is always exact, and requires no
X     * work.  Just adjust the address and length of the number to do
X     * the divide, but save the original pointer for freeing later.
X     */
X    zmul(tmp2, rp->mod, &tmp1);
X    zfree(tmp2);
X    zadd(z1, tmp1, &tmp2);
X    zfree(tmp1);
X    hp = tmp2.v;
X    if (tmp2.len <= rp->len) {
X        freeh(hp);
X        *res = _zero_;
X        return;
X    }
X    tmp2.v += rp->len;
X    tmp2.len -= rp->len;
X
X    /*
X     * Finally do a final modulo by a simple subtraction if necessary.
X     * This is all that is needed because the previous calculation is
X     * guaranteed to always be less than twice the modulus.
X     */
X    if (zrel(tmp2, rp->mod) < 0)
X        zcopy(tmp2, res);
X    else
X        zsub(tmp2, rp->mod, res);
X    freeh(hp);
X}
X
X
X/*
X * Multiply two numbers in REDC format together producing a result also
X * in REDC format.  If the result is converted back to a normal number,
X * then the result is the same as the modulo'd multiplication of the
X * original numbers before they were converted to REDC format.  This
X * calculation is done in one of two ways, depending on the size of the
X * modulus.  For large numbers, the REDC definition is used directly
X * which involves three multiplies overall.  For small numbers, a
X * complicated routine is used which does the indicated multiplication
X * and the REDC algorithm at the same time to produce the result.
X */
Xvoid
Xzredcmul(rp, z1, z2, res)
X    REDC *rp;        /* REDC information */
X    ZVALUE z1;        /* first REDC number to be multiplied */
X    ZVALUE z2;        /* second REDC number to be multiplied */
X    ZVALUE *res;        /* resulting REDC number */
X{
X    FULL mulb;
X    FULL muln;
X    HALF *h1;
X    HALF *h2;
X    HALF *h3;
X    HALF *hd;
X    HALF Ninv;
X    HALF topdigit;
X    LEN modlen;
X    LEN len;
X    LEN len2;
X    SIUNION sival1;
X    SIUNION sival2;
X    SIUNION sival3;
X    SIUNION carry;
X    ZVALUE tmp;
X
X    if (zisneg(z1) || (z1.len > rp->mod.len) ||
X        zisneg(z2) || (z2.len > rp->mod.len))
X            math_error("Negative or too large number in zredcmul");
X
X    /*
X     * Check for special values which we easily know the answer.
X     */
X    if (ziszero(z1) || ziszero(z2)) {
X        *res = _zero_;
X        return;
X    }
X
X    if ((z1.len == rp->one.len) && (z1.v[0] == rp->one.v[0]) &&
X        (zcmp(z1, rp->one) == 0)) {
X            zcopy(z2, res);
X            return;
X    }
X
X    if ((z2.len == rp->one.len) && (z2.v[0] == rp->one.v[0]) &&
X        (zcmp(z2, rp->one) == 0)) {
X            zcopy(z1, res);
X            return;
X    }
X
X    /*
X     * If the size of the modulus is large, then just do the multiply,
X     * followed by the two multiplies contained in the REDC routine.
X     * This will be quicker than directly doing the REDC calculation
X     * because of the O(N^1.585) speed of the multiplies.  The size
X     * of the number which this is done is configurable.
X     */
X    if (rp->mod.len >= _redc2_) {
X        zmul(z1, z2, &tmp);
X        zredcdecode(rp, tmp, res);
X        zfree(tmp);
X        return;
X    }
X
X    /*
X     * The number is small enough to calculate by doing the O(N^2) REDC
X     * algorithm directly.  This algorithm performs the multiplication and
X     * the reduction at the same time.  Notice the obscure facts that
X     * only the lowest word of the inverse value is used, and that
X     * there is no shifting of the partial products as there is in a
X     * normal multiply.
X     */
X    modlen = rp->mod.len;
X    Ninv = rp->inv.v[0];
X
X    /*
X     * Allocate the result and clear it.
X     * The size of the result will be equal to or smaller than
X     * the modulus size.
X     */
X    res->sign = 0;
X    res->len = modlen;
X    res->v = alloc(modlen);
X
X    hd = res->v;
X    len = modlen;
X    while (len--)
X        *hd++ = 0;
X
X    /*
X     * Do this outermost loop over all the digits of z1.
X     */
X    h1 = z1.v;
X    len = z1.len;
X    while (len--) {
X        /*
X         * Start off with the next digit of z1, the first
X         * digit of z2, and the first digit of the modulus.
X         */
X        mulb = (FULL) *h1++;
X        h2 = z2.v;
X        h3 = rp->mod.v;
X        hd = res->v;
X        sival1.ivalue = mulb * ((FULL) *h2++) + ((FULL) *hd++);
X        muln = ((HALF) (sival1.silow * Ninv));
X        sival2.ivalue = muln * ((FULL) *h3++);
X        sival3.ivalue = ((FULL) sival1.silow) + ((FULL) sival2.silow);
X        carry.ivalue = ((FULL) sival1.sihigh) + ((FULL) sival2.sihigh)
X            + ((FULL) sival3.sihigh);
X
X        /*
X         * Do this innermost loop for each digit of z2, except
X         * for the first digit which was just done above.
X         */
X        len2 = z2.len;
X        while (--len2 > 0) {
X            sival1.ivalue = mulb * ((FULL) *h2++);
X            sival2.ivalue = muln * ((FULL) *h3++);
X            sival3.ivalue = ((FULL) sival1.silow)
X                + ((FULL) sival2.silow)
X                + ((FULL) *hd)
X                + ((FULL) carry.silow);
X            carry.ivalue = ((FULL) sival1.sihigh)
X                + ((FULL) sival2.sihigh)
X                + ((FULL) sival3.sihigh)
X                + ((FULL) carry.sihigh);
X
X            hd[-1] = sival3.silow;
X            hd++;
X        }
X
X        /*
X         * Now continue the loop as necessary so the total number
X         * of interations is equal to the size of the modulus.
X         * This acts as if the innermost loop was repeated for
X         * high digits of z2 that are zero.
X         */
X        len2 = modlen - z2.len;
X        while (len2--) {
X            sival2.ivalue = muln * ((FULL) *h3++);
X            sival3.ivalue = ((FULL) sival2.silow)
X                + ((FULL) *hd)
X                + ((FULL) carry.silow);
X            carry.ivalue = ((FULL) sival2.sihigh)
X                + ((FULL) sival3.sihigh)
X                + ((FULL) carry.sihigh);
X
X            hd[-1] = sival3.silow;
X            hd++;
X        }
X
X        res->v[modlen - 1] = carry.silow;
X        topdigit = carry.sihigh;
X    }
X
X    /*
X     * Now continue the loop as necessary so the total number
X     * of interations is equal to the size of the modulus.
X     * This acts as if the outermost loop was repeated for high
X     * digits of z1 that are zero.
X     */
X    len = modlen - z1.len;
X    while (len--) {
X        /*
X         * Start off with the first digit of the modulus.
X         */
X        h3 = rp->mod.v;
X        hd = res->v;
X        muln = ((HALF) (*hd * Ninv));
X        sival2.ivalue = muln * ((FULL) *h3++);
X        sival3.ivalue = ((FULL) *hd++) + ((FULL) sival2.silow);
X        carry.ivalue = ((FULL) sival2.sihigh) + ((FULL) sival3.sihigh);
X
X        /*
X         * Do this innermost loop for each digit of the modulus,
X         * except for the first digit which was just done above.
X         */
X        len2 = modlen;
X        while (--len2 > 0) {
X            sival2.ivalue = muln * ((FULL) *h3++);
X            sival3.ivalue = ((FULL) sival2.silow)
X                + ((FULL) *hd)
X                + ((FULL) carry.silow);
X            carry.ivalue = ((FULL) sival2.sihigh)
X                + ((FULL) sival3.sihigh)
X                + ((FULL) carry.sihigh);
X
X            hd[-1] = sival3.silow;
X            hd++;
X        }
X        res->v[modlen - 1] = carry.silow;
X        topdigit = carry.sihigh;
X    }
X
X    /*
X     * Determine the true size of the result, taking the top digit of
X     * the current result into account.  The top digit is not stored in
X     * the number because it is temporary and would become zero anyway
X     * after the final subtraction is done.
X     */
X    if (topdigit == 0) {
X        len = modlen;
X        hd = &res->v[len - 1];
X        while ((*hd == 0) && (len > 1)) {
X            hd--;
X            len--;
X        }
X        res->len = len;
X    }
X
X    /*
X     * Compare the result with the modulus.
X     * If it is less than the modulus, then the calculation is complete.
X     */
X    if ((topdigit == 0) && ((len < modlen)
X        || (res->v[len - 1] < rp->mod.v[len - 1])
X        || (zrel(*res, rp->mod) < 0)))
X            return;
X
X    /*
X     * Do a subtraction to reduce the result to a value less than
X     * the modulus.  The REDC algorithm guarantees that a single subtract
X     * is all that is needed.  Ignore any borrowing from the possible
X     * highest word of the current result because that would affect
X     * only the top digit value that was not stored and would become
X     * zero anyway.
X     */
X    carry.ivalue = 0;
X    h1 = rp->mod.v;
X    hd = res->v;
X    len = modlen;
X    while (len--) {
X        carry.ivalue = BASE1 - ((FULL) *hd) + ((FULL) *h1++)
X            + ((FULL) carry.silow);
X        *hd++ = BASE1 - carry.silow;
X        carry.silow = carry.sihigh;
X    }
X
X    /*
X     * Now finally recompute the size of the result.
X     */
X    len = modlen;
X    hd = &res->v[len - 1];
X    while ((*hd == 0) && (len > 1)) {
X        hd--;
X        len--;
X    }
X    res->len = len;
X}
X
X
X/*
X * Square a number in REDC format producing a result also in REDC format.
X */
Xvoid
Xzredcsquare(rp, z1, res)
X    REDC *rp;        /* REDC information */
X    ZVALUE z1;        /* REDC number to be squared */
X    ZVALUE *res;        /* resulting REDC number */
X{
X    ZVALUE tmp;
X
X    if (zisneg(z1))
X        math_error("Negative number in zredcsquare");
X    if (ziszero(z1)) {
X        *res = _zero_;
X        return;
X    }
X    if ((z1.len == rp->one.len) && (z1.v[0] == rp->one.v[0]) &&
X        (zcmp(z1, rp->one) == 0)) {
X            zcopy(z1, res);
X            return;
X    }
X
X    /*
X     * If the modulus is small enough, then call the multiply
X     * routine to produce the result.  Otherwise call the O(N^1.585)
X     * routines to get the answer.
X     */
X    if (rp->mod.len < _redc2_) {
X        zredcmul(rp, z1, z1, res);
X        return;
X    }
X    zsquare(z1, &tmp);
X    zredcdecode(rp, tmp, res);
X    zfree(tmp);
X}
X
X
X/*
X * Compute the result of raising a REDC format number to a power.
X * The result is within the range 0 to the modulus - 1.
X * This calculates the result by examining the power POWBITS bits at a time,
X * using a small table of POWNUMS low powers to calculate powers for those bits,
X * and repeated squaring and multiplying by the partial powers to generate
X * the complete power.
X */
Xvoid
Xzredcpower(rp, z1, z2, res)
X    REDC *rp;        /* REDC information */
X    ZVALUE z1;        /* REDC number to be raised */
X    ZVALUE z2;        /* normal number to raise number to */
X    ZVALUE *res;        /* result */
X{
X    HALF *hp;        /* pointer to current word of the power */
X    ZVALUE *pp;        /* pointer to low power table */
X    ZVALUE ans, temp;    /* calculation values */
X    ZVALUE modpow;        /* current small power */
X    ZVALUE lowpowers[POWNUMS];    /* low powers */
X    int curshift;        /* shift value for word of power */
X    HALF curhalf;        /* current word of power */
X    unsigned int curpow;    /* current low power */
X    unsigned int curbit;    /* current bit of low power */
X    int i;
X
X    if (zisneg(z1))
X        math_error("Negative number in zredcpower");
X    if (zisneg(z2))
X        math_error("Negative power in zredcpower");
X
X    /*
X     * Check for zero or the REDC format for one.
X     */
X    if (ziszero(z1) || zisunit(rp->mod)) {
X        *res = _zero_;
X        return;
X    }
X    if (zcmp(z1, rp->one) == 0) {
X        zcopy(rp->one, res);
X        return;
X    }
X
X    /*
X     * See if the number being raised is the REDC format for -1.
X     * If so, then the answer is the REDC format for one or minus one.
X     * To do this check, calculate the REDC format for -1.
X     */
X    if (((HALF)(z1.v[0] + rp->one.v[0])) == rp->mod.v[0]) {
X        zsub(rp->mod, rp->one, &temp);
X        if (zcmp(z1, temp) == 0) {
X            if (zisodd(z2)) {
X                *res = temp;
X                return;
X            }
X            zfree(temp);
X            zcopy(rp->one, res);
X            return;
X        }
X        zfree(temp);
X    }
X
X    for (pp = &lowpowers[2]; pp < &lowpowers[POWNUMS]; pp++)
X        pp->len = 0;
X    zcopy(rp->one, &lowpowers[0]);
X    zcopy(z1, &lowpowers[1]);
X    zcopy(rp->one, &ans);
X
X    hp = &z2.v[z2.len - 1];
X    curhalf = *hp;
X    curshift = BASEB - POWBITS;
X    while (curshift && ((curhalf >> curshift) == 0))
X        curshift -= POWBITS;
X
X    /*
X     * Calculate the result by examining the power POWBITS bits at a time,
X     * and use the table of low powers at each iteration.
X     */
X    for (;;) {
X        curpow = (curhalf >> curshift) & (POWNUMS - 1);
X        pp = &lowpowers[curpow];
X
X        /*
X         * If the small power is not yet saved in the table, then
X         * calculate it and remember it in the table for future use.
X         */
X        if (pp->len == 0) {
X            if (curpow & 0x1)
X                zcopy(z1, &modpow);
X            else
X                zcopy(rp->one, &modpow);
X
X            for (curbit = 0x2; curbit <= curpow; curbit *= 2) {
X                pp = &lowpowers[curbit];
X                if (pp->len == 0)
X                    zredcsquare(rp, lowpowers[curbit/2],
X                        pp);
X                if (curbit & curpow) {
X                    zredcmul(rp, *pp, modpow, &temp);
X                    zfree(modpow);
X                    modpow = temp;
X                }
X            }
X            pp = &lowpowers[curpow];
X            *pp = modpow;
X        }
X
X        /*
X         * If the power is nonzero, then accumulate the small power
X         * into the result.
X         */
X        if (curpow) {
X            zredcmul(rp, ans, *pp, &temp);
X            zfree(ans);
X            ans = temp;
X        }
X
X        /*
X         * Select the next POWBITS bits of the power, if there is
X         * any more to generate.
X         */
X        curshift -= POWBITS;
X        if (curshift < 0) {
X            if (hp-- == z2.v)
X                break;
X            curhalf = *hp;
X            curshift = BASEB - POWBITS;
X        }
X
X        /*
X         * Square the result POWBITS times to make room for the next
X         * chunk of bits.
X         */
X        for (i = 0; i < POWBITS; i++) {
X            zredcsquare(rp, ans, &temp);
X            zfree(ans);
X            ans = temp;
X        }
X    }
X
X    for (pp = lowpowers; pp < &lowpowers[POWNUMS]; pp++) {
X        if (pp->len)
X            freeh(pp->v);
X    }
X    *res = ans;
X}
X
X/* END CODE */
SHAR_EOF
chmod 0644 calc2.9.0/zmod.c || echo "restore of calc2.9.0/zmod.c fails"
set `wc -c calc2.9.0/zmod.c`;Sum=$1
if test "$Sum" != "32540"
then echo original size 32540, current size $Sum;fi
echo "x - extracting calc2.9.0/zmul.c (Text)"
sed 's/^X//' << 'SHAR_EOF' > calc2.9.0/zmul.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 * Faster than usual multiplying and squaring routines.
X * The algorithm used is the reasonably simple one from Knuth, volume 2,
X * section 4.3.3.  These recursive routines are of speed O(N^1.585)
X * instead of O(N^2).  The usual multiplication and (almost usual) squaring
X * algorithms are used for small numbers.  On a 386 with its compiler, the
X * two algorithms are equal in speed at about 100 decimal digits.
X */
X
X#include "zmath.h"
X
X
XLEN _mul2_ = MUL_ALG2;        /* size of number to use multiply algorithm 2 */
XLEN _sq2_ = SQ_ALG2;        /* size of number to use square algorithm 2 */
X
X
Xstatic HALF *tempbuf;        /* temporary buffer for multiply and square */
X
Xstatic LEN domul MATH_PROTO((HALF *v1, LEN size1, HALF *v2, LEN size2, HALF *ans));
Xstatic LEN dosquare MATH_PROTO((HALF *vp, LEN size, HALF *ans));
X
X
X/*
X * Multiply two numbers using the following formula recursively:
X *    (A*S+B)*(C*S+D) = (S^2+S)*A*C + S*(A-B)*(D-C) + (S+1)*B*D
X * where S is a power of 2^16, and so multiplies by it are shifts, and
X * A,B,C,D are the left and right halfs of the numbers to be multiplied.
X */
Xvoid
Xzmul(z1, z2, res)
X    ZVALUE z1, z2;        /* numbers to multiply */
X    ZVALUE *res;        /* result of multiplication */
X{
X    LEN len;        /* size of array */
X
X    if (ziszero(z1) || ziszero(z2)) {
X        *res = _zero_;
X        return;
X    }
X    if (zisunit(z1)) {
X        zcopy(z2, res);
X        res->sign = (z1.sign != z2.sign);
X        return;
X    }
X    if (zisunit(z2)) {
X        zcopy(z1, res);
X        res->sign = (z1.sign != z2.sign);
X        return;
X    }
X
X    /*
X     * Allocate a temporary buffer for the recursion levels to use.
X     * An array needs to be allocated large enough for all of the
X     * temporary results to fit in.  This size is about twice the size
X     * of the largest original number, since each recursion level uses
X     * the size of its given number, and whose size is 1/2 the size of
X     * the previous level.  The sum of the infinite series is 2.
X     * Add some extra words because of rounding when dividing by 2
X     * and also because of the extra word that each multiply needs.
X     */
X    len = z1.len;
X    if (len < z2.len)
X        len = z2.len;
X    len = 2 * len + 64;
X    tempbuf = zalloctemp(len);
X
X    res->sign = (z1.sign != z2.sign);
X    res->v = alloc(z1.len + z2.len + 1);
X    res->len = domul(z1.v, z1.len, z2.v, z2.len, res->v);
X}
X
X
X/*
X * Recursive routine to multiply two numbers by splitting them up into
X * two numbers of half the size, and using the results of multiplying the
X * subpieces.  The result is placed in the indicated array, which must be
X * large enough for the result plus one extra word (size1 + size2 + 1).
X * Returns the actual size of the result with leading zeroes stripped.
X * This also uses a temporary array which must be twice as large as
X * one more than the size of the number at the top level recursive call.
X */
Xstatic LEN
Xdomul(v1, size1, v2, size2, ans)
X    HALF *v1;        /* first number */
X    LEN size1;        /* size of first number */
X    HALF *v2;        /* second number */
X    LEN size2;        /* size of second number */
X    HALF *ans;        /* location for result */
X{
X    LEN shift;        /* amount numbers are shifted by */
X    LEN sizeA;        /* size of left half of first number */
X    LEN sizeB;        /* size of right half of first number */
X    LEN sizeC;        /* size of left half of second number */
X    LEN sizeD;        /* size of right half of second number */
X    LEN sizeAB;        /* size of subtraction of A and B */
X    LEN sizeDC;        /* size of subtraction of D and C */
X    LEN sizeABDC;        /* size of product of above two results */
X    LEN subsize;        /* size of difference of halfs */
X    LEN copysize;        /* size of number left to copy */
X    LEN sizetotal;        /* total size of product */
X    LEN len;        /* temporary length */
X    HALF *baseA;        /* base of left half of first number */
X    HALF *baseB;        /* base of right half of first number */
X    HALF *baseC;        /* base of left half of second number */
X    HALF *baseD;        /* base of right half of second number */
X    HALF *baseAB;        /* base of result of subtraction of A and B */
X    HALF *baseDC;        /* base of result of subtraction of D and C */
X    HALF *baseABDC;        /* base of product of above two results */
X    HALF *baseAC;        /* base of product of A and C */
X    HALF *baseBD;        /* base of product of B and D */
X    FULL carry;        /* carry digit for small multiplications */
X    FULL carryACBD;        /* carry from addition of A*C and B*D */
X    FULL digit;        /* single digit multiplying by */
X    HALF *temp;        /* base for temporary calculations */
X    BOOL neg;        /* whether imtermediate term is negative */
X    register HALF *hd, *h1, *h2;    /* for inner loops */
X    SIUNION sival;        /* for addition of digits */
X
X    /*
X     * Trim the numbers of leading zeroes and initialize the
X     * estimated size of the result.
X     */
X    hd = &v1[size1 - 1];
X    while ((*hd == 0) && (size1 > 1)) {
X        hd--;
X        size1--;
X    }
X    hd = &v2[size2 - 1];
X    while ((*hd == 0) && (size2 > 1)) {
X        hd--;
X        size2--;
X    }
X    sizetotal = size1 + size2;
X
X    /*
X     * First check for zero answer.
X     */
X    if (((size1 == 1) && (*v1 == 0)) || ((size2 == 1) && (*v2 == 0))) {
X        *ans = 0;
X        return 1;
X    }
X
X    /*
X     * Exchange the two numbers if necessary to make the number of
X     * digits of the first number be greater than or equal to the
X     * second number.
X     */
X    if (size1 < size2) {
X        len = size1; size1 = size2; size2 = len;
X        hd = v1; v1 = v2; v2 = hd;
X    }
X
X    /*
X     * If the smaller number has only a few digits, then calculate
X     * the result in the normal manner in order to avoid the overhead
X     * of the recursion for small numbers.  The number of digits where
X     * the algorithm changes is settable from 2 to maxint.
X     */
X    if (size2 < _mul2_) {
X        /*
X         * First clear the top part of the result, and then multiply
X         * by the lowest digit to get the first partial sum.  Later
X         * products will then add into this result.
X         */
X        hd = &ans[size1];
X        len = size2;
X        while (len--)
X            *hd++ = 0;
X
X        digit = *v2++;
X        h1 = v1;
X        hd = ans;
X        carry = 0;
X        len = size1;
X        while (len >= 4) {    /* expand the loop some */
X            len -= 4;
X            sival.ivalue = ((FULL) *h1++) * digit + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X            sival.ivalue = ((FULL) *h1++) * digit + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X            sival.ivalue = ((FULL) *h1++) * digit + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X            sival.ivalue = ((FULL) *h1++) * digit + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X        while (len--) {
X            sival.ivalue = ((FULL) *h1++) * digit + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X        *hd = (HALF)carry;
X
X        /*
X         * Now multiply by the remaining digits of the second number,
X         * adding each product into the final result.
X         */
X        h2 = ans;
X        while (--size2 > 0) {
X            digit = *v2++;
X            h1 = v1;
X            hd = ++h2;
X            if (digit == 0)
X                continue;
X            carry = 0;
X            len = size1;
X            while (len >= 4) {    /* expand the loop some */
X                len -= 4;
X                sival.ivalue = ((FULL) *h1++) * digit
X                    + ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X                sival.ivalue = ((FULL) *h1++) * digit
X                    + ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X                sival.ivalue = ((FULL) *h1++) * digit
X                    + ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X                sival.ivalue = ((FULL) *h1++) * digit
X                    + ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X            }
X            while (len--) {
X                sival.ivalue = ((FULL) *h1++) * digit
X                    + ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X            }
X            while (carry) {
X                sival.ivalue = ((FULL) *hd) + carry;
X                *hd++ = sival.silow;
X                carry = sival.sihigh;
X            }
X        }
X
X        /*
X         * Now return the true size of the number.
X         */
X        len = sizetotal;
X        hd = &ans[len - 1];
X        while ((*hd == 0) && (len > 1)) {
X            hd--;
X            len--;
X        }
X        return len;
X    }
X
X    /*
X     * Need to multiply by a large number.
X     * Allocate temporary space for calculations, and calculate the
X     * value for the shift.  The shift value is 1/2 the size of the
X     * larger (first) number (rounded up).  The amount of temporary
X     * space needed is twice the size of the shift, plus one more word
X     * for the multiply to use.
X     */
X    shift = (size1 + 1) / 2;
X    temp = tempbuf;
X    tempbuf += (2 * shift) + 1;
X
X    /*
X     * Determine the sizes and locations of all the numbers.
X     * The value of sizeC can be negative, and this is checked later.
X     * The value of sizeD is limited by the full size of the number.
X     */
X    baseA = v1 + shift;
X    baseB = v1;
X    baseC = v2 + shift;
X    baseD = v2;
X    baseAB = ans;
X    baseDC = ans + shift;
X    baseAC = ans + shift * 2;
X    baseBD = ans;
X
X    sizeA = size1 - shift;
X    sizeC = size2 - shift;
X
X    sizeB = shift;
X    hd = &baseB[shift - 1];
X    while ((*hd == 0) && (sizeB > 1)) {
X        hd--;
X        sizeB--;
X    }
X
X    sizeD = shift;
X    if (sizeD > size2)
X        sizeD = size2;
X    hd = &baseD[sizeD - 1];
X    while ((*hd == 0) && (sizeD > 1)) {
X        hd--;
X        sizeD--;
X    }
X
X    /*
X     * If the smaller number has a high half of zero, then calculate
X     * the result by breaking up the first number into two numbers
X     * and combining the results using the obvious formula:
X     *    (A*S+B) * D = (A*D)*S + B*D
X     */
X    if (sizeC <= 0) {
X        len = domul(baseB, sizeB, baseD, sizeD, ans);
X        hd = &ans[len];
X        len = sizetotal - len;
X        while (len--)
X            *hd++ = 0;
X
X        /*
X         * Add the second number into the first number, shifted
X         * over at the correct position.
X         */
X        len = domul(baseA, sizeA, baseD, sizeD, temp);
X        h1 = temp;
X        hd = ans + shift;
X        carry = 0;
X        while (len--) {
X            sival.ivalue = ((FULL) *h1++) + ((FULL) *hd) + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X        while (carry) {
X            sival.ivalue = ((FULL) *hd) + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X
X        /*
X         * Determine the final size of the number and return it.
X         */
X        len = sizetotal;
X        hd = &ans[len - 1];
X        while ((*hd == 0) && (len > 1)) {
X            hd--;
X            len--;
X        }
X        tempbuf = temp;
X        return len;
X    }
X
X    /*
X     * Now we know that the high halfs of the numbers are nonzero,
X     * so we can use the complete formula.
X     *    (A*S+B)*(C*S+D) = (S^2+S)*A*C + S*(A-B)*(D-C) + (S+1)*B*D.
X     * The steps are done in the following order:
X     *    A-B
X     *    D-C
X     *    (A-B)*(D-C)
X     *    S^2*A*C + B*D
X     *    (S^2+S)*A*C + (S+1)*B*D                (*)
X     *    (S^2+S)*A*C + S*(A-B)*(D-C) + (S+1)*B*D
X     *
X     * Note: step (*) above can produce a result which is larger than
X     * the final product will be, and this is where the extra word
X     * needed in the product comes from.  After the final subtraction is
X     * done, the result fits in the expected size.  Using the extra word
X     * is easier than suppressing the carries and borrows everywhere.
X     *
X     * Begin by forming the product (A-B)*(D-C) into a temporary
X     * location that we save until the final step.  Do each subtraction
X     * at positions 0 and S.  Be very careful about the relative sizes
X     * of the numbers since this result can be negative.  For the first
X     * step calculate the absolute difference of A and B into a temporary
X     * location at position 0 of the result.  Negate the sign if A is
X     * smaller than B.
X     */
X    neg = FALSE;
X    if (sizeA == sizeB) {
X        len = sizeA;
X        h1 = &baseA[len - 1];
X        h2 = &baseB[len - 1];
X        while ((len > 1) && (*h1 == *h2)) {
X            len--;
X            h1--;
X            h2--;
X        }
X    }
X    if ((sizeA > sizeB) || ((sizeA == sizeB) && (*h1 > *h2)))
X    {
X        h1 = baseA;
X        h2 = baseB;
X        sizeAB = sizeA;
X        subsize = sizeB;
X    } else {
X        neg = !neg;
X        h1 = baseB;
X        h2 = baseA;
X        sizeAB = sizeB;
X        subsize = sizeA;
X    }
X    copysize = sizeAB - subsize;
X
X    hd = baseAB;
X    carry = 0;
X    while (subsize--) {
X        sival.ivalue = BASE1 - ((FULL) *h1++) + ((FULL) *h2++) + carry;
X        *hd++ = BASE1 - sival.silow;
X        carry = sival.sihigh;
X    }
X    while (copysize--) {
X        sival.ivalue = (BASE1 - ((FULL) *h1++)) + carry;
X        *hd++ = BASE1 - sival.silow;
X        carry = sival.sihigh;
X    }
X
X    hd = &baseAB[sizeAB - 1];
X    while ((*hd == 0) && (sizeAB > 1)) {
X        hd--;
X        sizeAB--;
X    }
X
X    /*
X     * This completes the calculation of abs(A-B).  For the next step
X     * calculate the absolute difference of D and C into a temporary
X     * location at position S of the result.  Negate the sign if C is
X     * larger than D.
X     */
X    if (sizeC == sizeD) {
X        len = sizeC;
X        h1 = &baseC[len - 1];
X        h2 = &baseD[len - 1];
X        while ((len > 1) && (*h1 == *h2)) {
X            len--;
X            h1--;
X            h2--;
X        }
X    }
X    if ((sizeC > sizeD) || ((sizeC == sizeD) && (*h1 > *h2)))
X    {
X        neg = !neg;
X        h1 = baseC;
X        h2 = baseD;
X        sizeDC = sizeC;
X        subsize = sizeD;
X    } else {
X        h1 = baseD;
X        h2 = baseC;
X        sizeDC = sizeD;
X        subsize = sizeC;
X    }
X    copysize = sizeDC - subsize;
X
X    hd = baseDC;
X    carry = 0;
X    while (subsize--) {
X        sival.ivalue = BASE1 - ((FULL) *h1++) + ((FULL) *h2++) + carry;
X        *hd++ = BASE1 - sival.silow;
X        carry = sival.sihigh;
X    }
X    while (copysize--) {
X        sival.ivalue = (BASE1 - ((FULL) *h1++)) + carry;
X        *hd++ = BASE1 - sival.silow;
X        carry = sival.sihigh;
X    }
X    hd = &baseDC[sizeDC - 1];
X    while ((*hd == 0) && (sizeDC > 1)) {
X        hd--;
X        sizeDC--;
X    }
X
X    /*
X     * This completes the calculation of abs(D-C).  Now multiply
X     * together abs(A-B) and abs(D-C) into a temporary location,
X     * which is preserved until the final steps.
X     */
X    baseABDC = temp;
X    sizeABDC = domul(baseAB, sizeAB, baseDC, sizeDC, baseABDC);
X
X    /*
X     * Now calculate B*D and A*C into one of their two final locations.
X     * Make sure the high order digits of the products are zeroed since
X     * this initializes the final result.  Be careful about this zeroing
X     * since the size of the high order words might be smaller than
X     * the shift size.  Do B*D first since the multiplies use one more
X     * word than the size of the product.  Also zero the final extra
X     * word in the result for possible carries to use.
X     */
X    len = domul(baseB, sizeB, baseD, sizeD, baseBD);
X    hd = &baseBD[len];
X    len = shift * 2 - len;
X    while (len--)
X        *hd++ = 0;
X
X    len = domul(baseA, sizeA, baseC, sizeC, baseAC);
X    hd = &baseAC[len];
X    len = sizetotal - shift * 2 - len + 1;
X    while (len--)
X        *hd++ = 0;
X
X    /*
X     * Now add in A*C and B*D into themselves at the other shifted
X     * position that they need.  This addition is tricky in order to
X     * make sure that the two additions cannot interfere with each other.
X     * Therefore we first add in the top half of B*D and the lower half
X     * of A*C.  The sources and destinations of these two additions
X     * overlap, and so the same answer results from the two additions,
X     * thus only two pointers suffice for both additions.  Keep the
X     * final carry from these additions for later use since we cannot
X     * afford to change the top half of A*C yet.
X     */
X    h1 = baseBD + shift;
X    h2 = baseAC;
X    carryACBD = 0;
X    len = shift;
X    while (len--) {
X        sival.ivalue = ((FULL) *h1) + ((FULL) *h2) + carryACBD;
X        *h1++ = sival.silow;
X        *h2++ = sival.silow;
X        carryACBD = sival.sihigh;
X    }
X
X    /*
X     * Now add in the bottom half of B*D and the top half of A*C.
X     * These additions are straightforward, except that A*C should
X     * be done first because of possible carries from B*D, and the
X     * top half of A*C might not exist.  Add in one of the carries
X     * from the previous addition while we are at it.
X     */
X    h1 = baseAC + shift;
X    hd = baseAC;
X    carry = carryACBD;
X    len = sizetotal - 3 * shift;
X    while (len--) {
X        sival.ivalue = ((FULL) *h1++) + ((FULL) *hd) + carry;
X        *hd++ = sival.silow;
X        carry = sival.sihigh;
X    }
X    while (carry) {
X        sival.ivalue = ((FULL) *hd) + carry;
X        *hd++ = sival.silow;
X        carry = sival.sihigh;
X    }
X
X    h1 = baseBD;
X    hd = baseBD + shift;
X    carry = 0;
X    len = shift;
X    while (len--) {
X        sival.ivalue = ((FULL) *h1++) + ((FULL) *hd) + carry;
X        *hd++ = sival.silow;
X        carry = sival.sihigh;
X    }
X    while (carry) {
X        sival.ivalue = ((FULL) *hd) + carry;
X        *hd++ = sival.silow;
X        carry = sival.sihigh;
X    }
X
X    /*
X     * Now finally add in the other delayed carry from the
X     * above addition.
X     */
X    hd = baseAC + shift;
X    while (carryACBD) {
X        sival.ivalue = ((FULL) *hd) + carryACBD;
X        *hd++ = sival.silow;
X        carryACBD = sival.sihigh;
X    }
X
X    /*
X     * Now finally add or subtract (A-B)*(D-C) into the final result at
X     * the correct position (S), according to whether it is positive or
X     * negative.  When subtracting, the answer cannot go negative.
X     */
X    h1 = baseABDC;
X    hd = ans + shift;
X    carry = 0;
X    len = sizeABDC;
X    if (neg) {
X        while (len--) {
X            sival.ivalue = BASE1 - ((FULL) *hd) +
X                ((FULL) *h1++) + carry;
X            *hd++ = BASE1 - sival.silow;
X            carry = sival.sihigh;
X        }
X        while (carry) {
X            sival.ivalue = BASE1 - ((FULL) *hd) + carry;
X            *hd++ = BASE1 - sival.silow;
X            carry = sival.sihigh;
X        }
X    } else {
X        while (len--) {
X            sival.ivalue = ((FULL) *h1++) + ((FULL) *hd) + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X        while (carry) {
X            sival.ivalue = ((FULL) *hd) + carry;
X            *hd++ = sival.silow;
X            carry = sival.sihigh;
X        }
X    }
X
X    /*
X     * Finally determine the size of the final result and return that.
X     */
X    len = sizetotal;
X    hd = &ans[len - 1];
X    while ((*hd == 0) && (len > 1)) {
X        hd--;
X        len--;
X    }
X    tempbuf = temp;
X    return len;
X}
X
X
X/*
X * Square a number by using the following formula recursively:
X *    (A*S+B)^2 = (S^2+S)*A^2 + (S+1)*B^2 - S*(A-B)^2
X * where S is a power of 2^16, and so multiplies by it are shifts,
X * and A and B are the left and right halfs of the number to square.
X */
Xvoid
Xzsquare(z, res)
X    ZVALUE z, *res;
X{
X    LEN len;
X
X    if (ziszero(z)) {
X        *res = _zero_;
X        return;
X    }
X    if (zisunit(z)) {
X        *res = _one_;
X        return;
X    }
X
X    /*
X     * Allocate a temporary array if necessary for the recursion to use.
X     * The array needs to be allocated large enough for all of the
X     * temporary results to fit in.  This size is about 3 times the
X     * size of the original number, since each recursion level uses 3/2
X     * of the size of its given number, and whose size is 1/2 the size
X     * of the previous level.  The sum of the infinite series is 3.
X     * Allocate some extra words for rounding up the sizes.
X     */
X    len = 3 * z.len + 32;
X    tempbuf = zalloctemp(len);
X
X    res->sign = 0;
X    res->v = alloc(z.len * 2);
X    res->len = dosquare(z.v, z.len, res->v);
X}
X
X
X/*
X * Recursive routine to square a number by splitting it up into two numbers
X * of half the size, and using the results of squaring the subpieces.
X * The result is placed in the indicated array, which must be large
X * enough for the result (size * 2).  Returns the size of the result.
X * This uses a temporary array which must be 3 times as large as the
X * size of the number at the top level recursive call.
X */
Xstatic LEN
Xdosquare(vp, size, ans)
X    HALF *vp;        /* value to be squared */
X    LEN size;        /* length of value to square */
X    HALF *ans;        /* location for result */
X{
X    LEN shift;        /* amount numbers are shifted by */
X    LEN sizeA;        /* size of left half of number to square */
X    LEN sizeB;        /* size of right half of number to square */
X    LEN sizeAA;        /* size of square of left half */
X    LEN sizeBB;        /* size of square of right half */
X    LEN sizeAABB;        /* size of sum of squares of A and B */
X    LEN sizeAB;        /* size of difference of A and B */
X    LEN sizeABAB;        /* size of square of difference of A and B */
X    LEN subsize;        /* size of difference of halfs */
X    LEN copysize;        /* size of number left to copy */
X    LEN sumsize;        /* size of sum */
X    LEN sizetotal;        /* total size of square */
X    LEN len;        /* temporary length */
X    LEN len1;        /* another temporary length */
X    FULL carry;        /* carry digit for small multiplications */
X    FULL digit;        /* single digit multiplying by */
X    HALF *temp;        /* base for temporary calculations */
X    HALF *baseA;        /* base of left half of number */
X    HALF *baseB;        /* base of right half of number */
X    HALF *baseAA;        /* base of square of left half of number */
X    HALF *baseBB;        /* base of square of right half of number */
X    HALF *baseAABB;        /* base of sum of squares of A and B */
X    HALF *baseAB;        /* base of difference of A and B */
X    HALF *baseABAB;        /* base of square of difference of A and B */
X    register HALF *hd, *h1, *h2, *h3;    /* for inner loops */
X    SIUNION sival;        /* for addition of digits */
X
X    /*
X     * First trim the number of leading zeroes.
SHAR_EOF
echo "End of part 13"
echo "File calc2.9.0/zmul.c is continued in part 14"
echo "14" > s2_seq_.tmp
exit 0