csl/embedded/arith06.c

/*  arith06.c                         Copyright (C) 1990-2008 Codemist Ltd */

/*
 * Arithmetic functions... lots of Lisp entrypoints.
 * note that for CSL I want plus and times to be special forms.
 */

/**************************************************************************
 * Copyright (C) 2008, Codemist Ltd.                     A C Norman       *
 *                                                                        *
 * Redistribution and use in source and binary forms, with or without     *
 * modification, are permitted provided that the following conditions are *
 * met:                                                                   *
 *                                                                        *
 *     * Redistributions of source code must retain the relevant          *
 *       copyright notice, this list of conditions and the following      *
 *       disclaimer.                                                      *
 *     * Redistributions in binary form must reproduce the above          *
 *       copyright notice, this list of conditions and the following      *
 *       disclaimer in the documentation and/or other materials provided  *
 *       with the distribution.                                           *
 *                                                                        *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS    *
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT      *
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS      *
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE         *
 * COPYRIGHT OWNERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,   *
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,   *
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS  *
 * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND *
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR  *
 * TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF     *
 * THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH   *
 * DAMAGE.                                                                *
 *************************************************************************/


/* Signature: 46797271 04-Jul-2009 */

#include "headers.h"


/*****************************************************************************/
/***              Lisp-callable versions of arithmetic functions           ***/
/*****************************************************************************/


Lisp_Object Ladd1(Lisp_Object nil, Lisp_Object a)
{
    if (is_fixnum(a))
    {   /* fixnums have data shifted left 4 bits */
        if (a == 0x7ffffff1)     /* The ONLY possible overflow case here  */
            a = make_one_word_bignum(0x08000000);
        else return onevalue((Lisp_Object)(a + 0x10));  /* the cheap case */
    }
    else a = plus2(a, fixnum_of_int(1));
    errexit();
    return onevalue(a);
}

Lisp_Object Lsub1(Lisp_Object nil, Lisp_Object a)
{
    if (is_fixnum(a))
    {   if (a == ~0x7ffffffe)     /* The ONLY possible overflow case here  */
            return make_one_word_bignum(int_of_fixnum(a) - 1);
        else return onevalue((Lisp_Object)(a - 0x10));
    }
    else a = plus2(a, fixnum_of_int(-1));
    errexit();
    return onevalue(a);
}

#ifdef COMMON
Lisp_Object Lfloat_2(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSL_IGNORE(nil);
    if (is_sfloat(b))
    {   double d = float_of_number(a);
        return onevalue(make_sfloat(d));
    }
    else if (!is_bfloat(b)) return aerror1("bad arg for float",  b);
    else
    {   double d = float_of_number(a);
        return onevalue(make_boxfloat(d, type_of_header(flthdr(b))));
    }
}
#endif

Lisp_Object Lfloat(Lisp_Object nil, Lisp_Object a)
{
    double d;
    CSL_IGNORE(nil);
    if (!is_number(a)) return aerror1("bad arg for float", a);
    d = float_of_number(a);
#ifdef COMMON
/* Do we REALLY want single precision by default here? */
    return onevalue(make_boxfloat(d, TYPE_SINGLE_FLOAT));
#else
    return onevalue(make_boxfloat(d, TYPE_DOUBLE_FLOAT));
#endif
}

Lisp_Object Llognot(Lisp_Object nil, Lisp_Object a)
{
    a = lognot(a);
    errexit();
    return onevalue(a);
}

Lisp_Object Lash(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    a = ash(a, b);
    errexit();
    return onevalue(a);
}

Lisp_Object Lash1(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
/*
 * This function multiplies or divides by a power of two. Note that
 * this corresponds to natural shifts on a sign-and-magnitude machine,
 * but is not an "arithmetic" shift as that term is understood on
 * 2's complement machines.
 */
{
    CSLbool negative = NO;
    if (!is_fixnum(b)) return aerror("ash1");
    if (minusp(a))
    {   negative = YES;
        a = negate(a);
    }
    errexit();
    a = ash(a, b);
    errexit();
    if (negative)
    {   a = negate(a);
        errexit();
    }
    return onevalue(a);
}

static int msd_table[256] =
{
    0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
    5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
    6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
    6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
    7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
    7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
    7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
    7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
    8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
};

Lisp_Object Lmsd(Lisp_Object nil, Lisp_Object a)
{
    int32_t top;
    int32_t r = 0;
    CSL_IGNORE(nil);
    if (is_fixnum(a)) top = int_of_fixnum(a);
    else if (is_numbers(a))
    {   Header h = numhdr(a);
        if (!is_bignum_header(h)) return aerror1("bad arg for msd", a);
        r = (length_of_header(h)-CELL)/4 - 1;
        top = bignum_digits(a)[r];
        r = 31*r;
    }
    else return aerror1("bad arg for msd", a);
    if (top < 0) return aerror1("negative arg for msd", a);   /* -ve arg */
/*
 * Note that top may be zero here, but in that case the next word down of
 * the bignum involved MUST be fully normalised with its top bit set.
 * The effect of this code is that I return (msd 0) => 0.
 */
    if (top >= 0x10000) r += 16, top >>= 16;
    if (top >= 0x100)   r += 8,  top >>= 8;
    return onevalue(fixnum_of_int(r + msd_table[top]));
}

static int lsd_table[256] =
{
    8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

Lisp_Object Llsd(Lisp_Object nil, Lisp_Object a)
{
    int32_t top;
    int32_t r = 0;
    CSL_IGNORE(nil);
    if (is_fixnum(a))
    {   top = int_of_fixnum(a);
/* lsd(0) is taken to have the value 0 here - it is a bit of an odd case */
        if (top == 0) return onevalue(a);
    }
    else if (is_numbers(a))
    {   Header h = numhdr(a);
        if (!is_bignum_header(h)) return aerror1("bad arg for lsd", a);
        while ((top = bignum_digits(a)[r]) == 0) r++;
        r = 31*r;
    }
    else return aerror1("bad arg for lsd", a);
    if (top < 0) return aerror1("negative arg for lsd", a);   /* -ve arg */
/* top is non-zero here */
    if ((top & 0xffffu) == 0) r += 16, top >>= 16;
    if ((top & 0xff) == 0)    r += 8,  top >>= 8;
    return onevalue(fixnum_of_int(r + lsd_table[top & 0xff]));
}

Lisp_Object Linorm(Lisp_Object nil, Lisp_Object a, Lisp_Object k)
/*
 * This is a piece of magic especially designed to speed up the
 * REDUCE big-float code.  It adjusts the integer a until it has
 * just k bits, and returns a correction to the associated exponent.
 * It combines aspects of msd, lsd, ash and a rounding operation.
 */
{
    int32_t top, bottom, kk, bits;
    int32_t rtop = 0, rbottom = 0;
    CSLbool was_fixnum = NO, was_negative = NO, round_up;
    if (is_fixnum(k) && (int32_t)k >= 0) kk = int_of_fixnum(k);
    else return aerror1("bad args for inorm", k);
    if (is_fixnum(a))
    {   top = int_of_fixnum(a);
        if (top == 0) return aerror1("zero arg for inorm", a);
        bottom = top;
        was_fixnum = YES;
    }
    else if (is_numbers(a))
    {   Header h = numhdr(a);
        if (!is_bignum_header(h)) return aerror1("bad arg for inorm", a);
        rtop = (length_of_header(h)-CELL)/4 - 1;
        top = bignum_digits(a)[rtop];
        was_negative = (top < 0);
        rtop = 31*rtop;
        while ((bottom = bignum_digits(a)[rbottom]) == 0) rbottom++;
        rbottom = 31*rbottom;
    }
    else return aerror1("bad arg for inorm", a);
    if (top < 0) top = ~top;  /* Now top is guaranteed positive */
    if (top >= 0x10000) rtop += 16, top >>= 16;
    if (top >= 0x100)   rtop += 8,  top >>= 8;
    rtop = rtop + msd_table[top];
    if ((bottom & 0xffffu) == 0) rbottom += 16, bottom >>= 16;
    if ((bottom & 0xff) == 0)    rbottom += 8,  bottom >>= 8;
    rbottom = rbottom + lsd_table[bottom & 0xff];
/*
 * The next line adjusts for the odd case where the input number is
 * minus an exact power of 2, in which case finding its most significant bit
 * involved just a little correction.
 */
    round_up = was_negative;
    if (rtop == rbottom) rtop++;
    bits = rtop - rbottom;             /* bits used in the number */
    if (bits <= kk) kk = rbottom;      /* no rounding wanted      */
    else if (was_fixnum)
    {   int bit;
/*
 * If the input was a fixnum and I need to decrease its precision
 * I will do it in-line here, mainly so that the bignum code that comes
 * later will not have to worry so much about the possibility of having
 * any fixnums around.
 */
        kk = rtop - kk;
        bit = ((int32_t)1) << (kk - 1);
        top = int_of_fixnum(a);
        if (top < 0)
        {   top = -top;
/*
 * It is almost the case that for negative values I should round if the
 * bit I want to test is a zero (rather than a 1), but this is not true when
 * the bit involved is the least significant set bit in the word.  So to
 * keep it simple I negate, test, adjust and negate back when working with
 * single precision numbers.  I also do the shifting right on the positive
 * value to avoid problems with the bits that get shifted off, and with
 * computers where right shifts are logical rather than arithmetic.
 */
            if ((top & bit) != 0) top += bit;
            top = top >> kk;
            top = -top;
        }
        else
        {   if ((top & bit) != 0) top += bit;
            top = top >> kk;
        }
/*
 * All the shifts I do here move only zero bits off the bottom of the
 * word, and so there are no issues about +ve vs -ve numbers to bother me.
 */
        while ((top & 0xf) == 0)
        {   top = top >> 4;
#ifdef SIGNED_SHIFTS_ARE_LOGICAL
            if (top & 0x08000000) top |= ~0x0fffffff;
#endif
            kk += 4;
        }
        while ((top & 0x1) == 0)
        {   top = top >> 1;
#ifdef SIGNED_SHIFTS_ARE_LOGICAL
            if (top & 0x40000000) top |= ~0x7fffffff;
#endif
            kk += 1;
        }
        a = cons(fixnum_of_int(top), fixnum_of_int(kk));
        errexit();
        return onevalue(a);
    }
    else
    {   int32_t wk, bk;
/*
 * Here my input was a bignum and I have established that I not only need
 * to shift it right but that I will need to lose some non-zero digits from
 * the right hand end. To cope with this I need to decide whether it will
 * round up or down, and then perform the appropriate shifts, including a
 * post-normalisation to ensure that the mantissa of the number as returned
 * is odd.
 */
        kk = rtop - kk;
        if (rbottom == kk-1) round_up = YES;
        else
        {   int32_t wk1 = (kk-1) / 31, bk1 = (kk-1) % 31;
            int32_t bit = ((int32_t)1) << bk1;
            round_up = ((bit & bignum_digits(a)[wk1]) != 0);
            if (was_negative) round_up = !round_up;
        }
/*
 * Now I need to find out how much I will need to shift AFTER rounding
 * and truncation to leave me with a properly normalised value.
 */
        wk = kk / 31, bk = kk % 31;
/*
 * If I have a positive value that is not being rounded up I want to skip
 * over 0 bits until I find a 1. Similarly for a negative value that is
 * being rounded up.
 */
        if (was_negative == round_up)
        {
            for (;;)
            {   int32_t bit = ((int32_t)1) << bk;
                if ((bignum_digits(a)[wk] & bit) != 0) break;
                kk++;
                bk++;
                if (bk == 31) bk = 0, wk++;
            }
        }
        else
/*
 * A positive value that is being rounded up or a negative one that is not
 * should cause me to skip over 1 bits until I find a 0.  The 0 I find
 * will be promoted into a 1 achieve the rounding I need.
 */
        {
            for (;;)
            {   int32_t bit = ((int32_t)1) << bk;
                if ((bignum_digits(a)[wk] & bit) == 0) break;
                kk++;
                bk++;
                if (bk == 31) bk = 0, wk++;
            }
        }
    }
    if (kk != 0)
    {   a = ash(a, fixnum_of_int(-kk));
        errexit();
/*
 * All the adjustment I now need to allow for right-shifting negative
 * numbers and rounding off - at all reduces to just forcing the bottom bit
 * of the result I compute here to be a 1!
 */
        if (is_fixnum(a)) a |= 0x10;
        else bignum_digits(a)[0] |= 1;
    }
    a = cons(a, fixnum_of_int(kk));
    errexit();
    return onevalue(a);
}

#ifdef COMMON
/*
 * Implemented as a special form for Standard Lisp. Must be a regular
 * function in Common Lisp.
 */

static Lisp_Object MS_CDECL Lplus(Lisp_Object nil, int nargs, ...)
/*
 * This adds up a whole bunch of numbers together.
 *    (+ a1 a2 a3 a4 a5)                     is computed as
 *    (+ a1 (+ a2 (* a3 (+ a4 a5))))
 */
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs == 0) return fixnum_of_int(0);
    va_start(a, nargs);
    push_args(a, nargs);
/*
 * The actual args have been passed a C args - I can not afford to
 * risk garbage collection until they have all been moved somewhere safe,
 * and here that safe place is the Lisp stack.  I have to delay checking for
 * overflow on same until all args have been pushed.
 */
    stackcheck0(nargs);
    pop(r);
    nil = C_nil;
    for (i = 1; i<nargs; i++)
    {   Lisp_Object w;
        pop(w);
        if (is_fixnum(r) && is_fixnum(w))
        {   int32_t c = int_of_fixnum(r) + int_of_fixnum(w);
            int32_t w1 = c & fix_mask;
            if (w1 == 0 || w1 == fix_mask)
            {   r = fixnum_of_int(c);
                continue;
            }
        }
        r = plus2(r, w);
        errexitn(nargs-i);
    }
    return onevalue(r);
}

static Lisp_Object MS_CDECL Ldifference(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    Lisp_Object r;
    int i;
    if (nargs == 0) return onevalue(fixnum_of_int(0));
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    nil = C_nil;
    if (nargs == 1)
    {   pop(r);
        r = negate(r);
        errexit();
        return onevalue(r);
    }
    r = stack[1-nargs];
/*
 * (- a1 a2 a3 a4) is computed as
 * (((a1 - a4) - a3) - a2) which does not seem too bad here.
 */
    for (i=1; i<nargs; i++)
    {   Lisp_Object w;
        pop(w);
        r = difference2(r, w);
        errexitn(nargs-i);
    }
    popv(1);
    return onevalue(r);
}

static Lisp_Object MS_CDECL Ltimes(Lisp_Object nil, int nargs, ...)
/*
 * This multiplies a whole bunch of numbers together.
 */
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs == 0) return fixnum_of_int(1);
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    pop(r);
    nil = C_nil;
    for (i=1; i<nargs; i++)
    {   Lisp_Object w;
        pop(w);
        r = times2(r, w);
        errexitn(nargs-i);
    }
    return onevalue(r);
}

Lisp_Object MS_CDECL Lquotient_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    Lisp_Object r;
    int i;
    if (nargs == 0) return onevalue(fixnum_of_int(1));
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    if (nargs == 1)
    {   pop(r);
        r = CLquot2(fixnum_of_int(1), r);
        errexit();
        return onevalue(r);
    }
    r = stack[1-nargs];
    for (i=1; i<nargs; i++)
    {   Lisp_Object w;
        pop(w);
        r = CLquot2(r, w);
        errexitn(nargs-i);
    }
    popv(1);
    return onevalue(r);
}

Lisp_Object Lquotient(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    a = CLquot2(a, b);
    errexit();
    return onevalue(a);
}

static Lisp_Object LSLquotient(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    a = quot2(a, b);
    errexit();
    return onevalue(a);
}

Lisp_Object Lquotient_1(Lisp_Object nil, Lisp_Object b)
{
    b = CLquot2(fixnum_of_int(1), b);
    errexit();
    return onevalue(b);
}

#else  /* COMMON */

Lisp_Object Lquotient(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    a = quot2(a, b);
    errexit();
    return onevalue(a);
}

#endif /* COMMON */

Lisp_Object Ldivide(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    Lisp_Object q, r;
    stackcheck2(0, a, b);
    push2(a, b);
    q = quot2(a, b);
    pop2(b, a);
    errexit();
    push(q);
    r = Cremainder(a, b);
    pop(q);
    errexit();
    q = cons(q, r);
    errexit();
    return onevalue(q);
}

Lisp_Object Lrem(Lisp_Object nil, Lisp_Object p, Lisp_Object q)
{
    p = Cremainder(p, q);
    errexit();
    return onevalue(p);
}

Lisp_Object Lmod(Lisp_Object nil, Lisp_Object p, Lisp_Object q)
{
    p = modulus(p, q);
    errexit();
    return onevalue(p);
}

Lisp_Object Lplus2(Lisp_Object nil, Lisp_Object p, Lisp_Object q)
{
    if (is_fixnum(p) && is_fixnum(q))
    {   int32_t c = int_of_fixnum(p) + int_of_fixnum(q);
        int32_t w = c & fix_mask;
        if (w == 0 || w == fix_mask) return onevalue(fixnum_of_int(c));
    }
    p = plus2(p, q);
    errexit();
    return onevalue(p);
}

Lisp_Object Ltimes2(Lisp_Object nil, Lisp_Object p,
                        Lisp_Object q)
{
    p = times2(p, q);
    errexit();
    return onevalue(p);
}

Lisp_Object Ldifference2(Lisp_Object nil, Lisp_Object a,
                        Lisp_Object b)
{
    a = difference2(a, b);
    errexit();
    return onevalue(a);
}

Lisp_Object Lminus(Lisp_Object nil, Lisp_Object a)
{
    a = negate(a);
    errexit();
    return onevalue(a);
}

typedef Lisp_Object boolopfn(Lisp_Object, Lisp_Object);

static struct bfz { boolopfn *fn; Lisp_Object base; } boolop_array[] =
{
    {0,         0},
    {logand2,   fixnum_of_int(-1)},
    {0,         0},
    {0,         0},
    {0,         0},
    {0,         0},
    {logxor2,   fixnum_of_int(0)},
    {logior2,   fixnum_of_int(0)},
    {0,         0},
    {logeqv2,   fixnum_of_int(-1)},
    {0,         0},
    {0,         0},
    {0,         0},
    {0,         0},
    {0,         0},
    {0,         0}
};


static Lisp_Object MS_CDECL Lboolfn(Lisp_Object env, int nargs, ...)
{
    va_list a;
    Lisp_Object nil = C_nil, r;
    int i;
    int32_t what = int_of_fixnum(env);
    if (nargs == 0) return onevalue(boolop_array[what].base);
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    pop(r);
    for (i=1; i<nargs; i++)
    {   Lisp_Object w;
        pop(w);
        r = (*boolop_array[what].fn)(r, w);
        errexitn(nargs-i);
    }
    return onevalue(r);
}

Lisp_Object Lzerop(Lisp_Object nil, Lisp_Object a)
{
    CSLbool fg;
    fg = zerop(a);
    errexit();
    return onevalue(Lispify_predicate(fg));
}

Lisp_Object Lonep(Lisp_Object nil, Lisp_Object a)
{
    CSLbool fg;
    fg = onep(a);
    errexit();
    return onevalue(Lispify_predicate(fg));
}

Lisp_Object Levenp(Lisp_Object nil, Lisp_Object a)
{
    switch ((int)a & TAG_BITS)
    {
case TAG_FIXNUM:
        return onevalue(((int32_t)a & 0x10) == 0 ? lisp_true : nil);
case TAG_NUMBERS:
        if (is_bignum(a))
            return onevalue((bignum_digits(a)[0] & 1) == 0 ? lisp_true : nil);
        /* else drop through */
default:
        return aerror1("bad arg for evenp", a);
    }
}

Lisp_Object Loddp(Lisp_Object nil, Lisp_Object a)
{
    switch ((int)a & TAG_BITS)
    {
case TAG_FIXNUM:
        return onevalue(((int32_t)a & 0x10) != 0 ? lisp_true : nil);
case TAG_NUMBERS:
        if (is_bignum(a))
            return onevalue((bignum_digits(a)[0] & 1) != 0 ? lisp_true : nil);
        /* else drop through */
default:
        return aerror1("oddp", a);
    }
}

Lisp_Object Lminusp(Lisp_Object nil, Lisp_Object a)
{
/*
 * For CSL I demand (minusp <non-number>) = nil.  Note that this ensures
 * that minusp will not fail... so nil wil be intact on the way out.
 */
    return onevalue(is_number(a) && minusp(a) ? lisp_true : nil);
}

Lisp_Object Lplusp(Lisp_Object nil, Lisp_Object a)
{
    return onevalue(is_number(a) && plusp(a) ? lisp_true : nil);
}

/*
 * The next few functions take an arbitrary number of args in Common
 * Lisp mode but just 2 args in CSL.
 */

#ifdef COMMON

Lisp_Object MS_CDECL Leqn_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 2) return onevalue(lisp_true);
    if (nargs > ARG_CUT_OFF) return aerror("too many args for =");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool w = numeq2(r, s);
        nil = C_nil;
        if (exception_pending()) { popv(nargs); return nil; }
        if (!w)
        {   popv(nargs);
            return onevalue(nil);
        }
        r = s;
    }
    popv(nargs);
    return onevalue(lisp_true);
}

Lisp_Object Leqn(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = numeq2(a, b);
    errexit();
    return onevalue(w ? lisp_true : nil);
}

Lisp_Object Leqn_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

Lisp_Object MS_CDECL Llessp_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 2) return onevalue(lisp_true);
    if (nargs > ARG_CUT_OFF) return aerror("too many args for <");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool w = lessp2(r, s);
        nil = C_nil;
        if (exception_pending()) { popv(nargs); return nil; }
        if (!w)
        {   popv(nargs);
            return onevalue(nil);
        }
        r = s;
    }
    popv(nargs);
    return onevalue(lisp_true);
}

Lisp_Object Llessp(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = lessp2(a, b);
    errexit();
    return onevalue(w ? lisp_true : nil);
}

Lisp_Object Llessp_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

Lisp_Object MS_CDECL Lgreaterp_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 2) return onevalue(lisp_true);
    if (nargs > ARG_CUT_OFF) return aerror("too many args for >");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool w = lessp2(s, r);
        nil = C_nil;
        if (exception_pending()) { popv(nargs); return nil; }
        if (!w)
        {   popv(nargs);
            return onevalue(nil);
        }
        r = s;
    }
    popv(nargs);
    return onevalue(lisp_true);
}

Lisp_Object Lgreaterp(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = lessp2(b, a);
    errexit();
    return onevalue(w ? lisp_true : nil);
}

Lisp_Object Lgreaterp_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

static Lisp_Object MS_CDECL Lneqn(Lisp_Object nil, int nargs, ...)
/*
 * /= is supposed to check that NO pair of args match.
 */
{
    int i, j;
    Lisp_Object *r;
    va_list a;
    if (nargs < 2) return onevalue(lisp_true);
    r = (Lisp_Object *)&work_1;
    if (nargs > ARG_CUT_OFF) return aerror("too many args for /=");
    va_start(a, nargs);
    for (i=0; i<nargs; i++) r[i] = va_arg(a, Lisp_Object);
    va_end(a);
/*
 * This bit is OK provided numeq2 does not mess with work_1, ...
 * and I think that unless funny tracing or errors occur that should
 * be OK.
 */
    for (i = 1; i<nargs; i++)
    {   Lisp_Object n1 = r[i];
        for (j=0; j<i; j++)
        {   Lisp_Object n2 = r[j];
            CSLbool w = numeq2(n1, n2);
            nil = C_nil;
            if (exception_pending()) return nil;
            if (w) return onevalue(nil);
        }
    }
    return onevalue(lisp_true);
}

Lisp_Object Lneq_2(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = numeq2(a, b);
    errexit();
    return onevalue(w ? nil : lisp_true);
}

Lisp_Object Lneq_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

Lisp_Object MS_CDECL Lgeq_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 2) return onevalue(lisp_true);
    if (nargs > ARG_CUT_OFF) return aerror("too many args for >=");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool w = lesseq2(s, r);
        nil = C_nil;
        if (exception_pending()) { popv(nargs); return nil; }
        if (!w)
        {   popv(nargs);
            return onevalue(nil);
        }
        r = s;
    }
    popv(nargs);
    return onevalue(lisp_true);
}

Lisp_Object Lgeq(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = lesseq2(b, a);
    errexit();
    return onevalue(w ? lisp_true : nil);
}

Lisp_Object Lgeq_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

Lisp_Object MS_CDECL Lleq_n(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 2) return onevalue(lisp_true);
    if (nargs > ARG_CUT_OFF) return aerror("too many args for <=");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool fg = lesseq2(r, s);
        nil = C_nil;
        if (exception_pending()) { popv(nargs); return nil; }
        if (!fg)
        {   popv(nargs);
            return onevalue(nil);
        }
        r = s;
    }
    popv(nargs);
    return onevalue(lisp_true);
}

Lisp_Object Lleq(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w = lesseq2(a, b);
    errexit();
    return onevalue(w ? lisp_true : nil);
}

Lisp_Object Lleq_1(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    CSL_IGNORE(a);
    return onevalue(lisp_true);
}

#else /* COMMON */


Lisp_Object Leqn(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool r;
    r = numeq2(a, b);
    errexit();
    return onevalue(Lispify_predicate(r));
}

Lisp_Object Llessp(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool r;
/*
 * I have strongish expectations that fixnum arithmetic is so imporant that
 * it is worth lifting the fixnum comparison up here.
 */
    if (is_fixnum(a) && is_fixnum(b))
        return onevalue(Lispify_predicate((int32_t)a<(int32_t)b));
    r = lessp2(a, b);
    errexit();
    return onevalue(Lispify_predicate(r));
}

Lisp_Object Lgreaterp(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool r;
    if (is_fixnum(a) && is_fixnum(b))
        return onevalue(Lispify_predicate((int32_t)a>(int32_t)b));
    r = lessp2(b, a);
    errexit();
    return onevalue(Lispify_predicate(r));
}

Lisp_Object Lgeq(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool r;
    if (is_fixnum(a) && is_fixnum(b))
        return onevalue(Lispify_predicate((int32_t)a>=(int32_t)b));
    r = lessp2(a, b);
    errexit();
    return onevalue(Lispify_predicate(!r));
}

Lisp_Object Lleq(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool r;
    if (is_fixnum(a) && is_fixnum(b))
        return onevalue(Lispify_predicate((int32_t)a<=(int32_t)b));
    r = lessp2(b, a);
    errexit();
    return onevalue(Lispify_predicate(!r));
}

#endif /* COMMON */

Lisp_Object Lmax2(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w;
    CSL_IGNORE(nil);
    push2(a, b);
    w = lessp2(a, b);
    pop2(b, a);
    errexit();
    if (w) return onevalue(b);
    else return onevalue(a);
}

Lisp_Object Lmin2(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
    CSLbool w;
    CSL_IGNORE(nil);
    push2(a, b);
    w = lessp2(b, a);
    pop2(b, a);
    errexit();
    if (w) return onevalue(b);
    else return onevalue(a);
}

Lisp_Object MS_CDECL Lmax(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 1) return aerror("max");
    if (nargs > ARG_CUT_OFF) return aerror("too many args for max");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool fg;
        push2(r, s);
        fg = lessp2(r, s);
        pop2(s, r);
        nil = C_nil;
        if (exception_pending())
        {   popv(nargs);
            return nil;
        }
        if (fg) r = s;
    }
    popv(nargs);
    return onevalue(r);
}

Lisp_Object MS_CDECL Lmin(Lisp_Object nil, int nargs, ...)
{
    va_list a;
    int i;
    Lisp_Object r;
    if (nargs < 1) return aerror("min");
    if (nargs > ARG_CUT_OFF) return aerror("too many args for min");
    va_start(a, nargs);
    push_args(a, nargs);
    stackcheck0(nargs);
    r = stack[1-nargs];
    for (i = 1; i<nargs; i++)
    {   Lisp_Object s = stack[1+i-nargs];
        CSLbool fg;
        push2(r, s);
        fg = lessp2(s, r);
        pop2(s, r);
        nil = C_nil;
        if (exception_pending())
        {   popv(nargs);
            return nil;
        }
        if (fg) r = s;
    }
    popv(nargs);
    return onevalue(r);
}

Lisp_Object Lrational(Lisp_Object nil, Lisp_Object a)
{
    a = rational(a);
    errexit();
    return onevalue(a);
}

#ifdef COMMON

static Lisp_Object Lmanexp(Lisp_Object nil, Lisp_Object a)
{
    int x;
    double f;
    if (! is_float(a))  aerror1("arg is not a floating-point number", a);
    f = float_of_number(a);
    f = frexp(f, &x);
    errexit();
    return onevalue(cons(make_boxfloat(f,TYPE_DOUBLE_FLOAT),
                         fixnum_of_int(x)));
}

static Lisp_Object Lrationalize(Lisp_Object nil, Lisp_Object a)
{
    a = rationalize(a);
    errexit();
    return onevalue(a);
}
#endif

/*
 * The following random number generator is taken from the Norcroft
 * C library, but is included here so that random sequences will be
 * identical across all implementations of CSL, and because I have bad
 * and pessimistic expectations about the quality of random number
 * generators built into typical C libraries. That is not to say that
 * I ought not to be somewhat cynical about the code I have implemented
 * here! But it is tolerably fast and less dreadful than those old
 * 32-bit linear congruential mistakes. The initial values here
 * are a repeatable set of initial "random" values.
 */

static uint32_t random_number_seed[55] =
{
    0x0d649239,    0x7c09f002,    0x6da2cd88,    0x969df534,
    0xfd7aca32,    0x16d89669,    0xc334a2fc,    0x0aba529c,
    0xdea5e90d,    0xdf06db3b,    0xf07d65eb,    0x74a5bf84,
    0x81e0b59e,    0xf2ac7c6c,    0x14339237,    0xb6b89675,
    0x61a66ca1,    0xa3fd9c3c,    0xed3ed908,    0xb4ffaf68,
    0xe43adf58,    0x6c108373,    0x14bbefe5,    0x20045563,
    0x8c54d44e,    0xd3470877,    0x5a8ae401,    0xa38c47fd,
    0x70ec616e,    0x3a8e3c82,    0x5bf48b37,    0x98d07ad8,
    0x6753e8c1,    0xc120d571,    0x7d308c18,    0x014ef96d,
    0x7aae7f25,    0x817e97c8,    0x8127a883,    0x1f88de19,
    0x68c2f294,    0x394ea2dd,    0x2f475077,    0x1fbea2a6,
    0x6e943040,    0xfa736fbb,    0x89e5fc31,    0xca16186e,
    0x720e8da7,    0xd8c0b092,    0xb340e967,    0x6e0ba043,
    0x1250d232,    0x061a9e86,    0xaa710c75
};

static int random_j = 23, random_k = 54;

static CSLbool randomization_request = NO;

/*
 * If the user specifies a random number seed of zero I will try to
 * start things in as unpredictable a state as I reasonably can. To
 * achieve this I will update a block of unpredictable data at a
 * number of points during a CSL run, garnering incremental amounts
 * of fairly low grade "randomness" from timing information and the
 * memory addresses that get allocated to CSL. Because it will take
 * a while for such information to build up I arrange that specifying
 * a random seed of zero does not do anything at once (and in particular
 * the implicit call of this nature when CSL starts does not do much),
 * but the unpredictable mess I accumulate is inspected the first time
 * any user actually asks for a random value. Since user keyboard input
 * contributes to the clutter it could be that a cautious user will ask the
 * user to type in a long string of gibberish before asking for any
 * random numbers, and the gibberish typed will then in fact form part
 * of the seed that will be used.  On Windows I can hook in and make
 * mouse activity etc contribute to the seed too.
 */

static void randomize(void)
{
    int i;
    random_j = 23;
    random_k = 54;
    for (i=20; i<48; i+=4)
    {   CSL_MD5_Init();
        CSL_MD5_Update(unpredictable, sizeof(unpredictable));
        CSL_MD5_Final((unsigned char *)&random_number_seed[i]);
        inject_randomness((int)time(NULL));
    }
/*
 * Note that I do not initialise the whole array of seed values here.
 * Leaving something over can count as part of the unpredictability! But I
 * do try to put in mess through the parts of the seed that will be used
 * first so that any obvious patterns will get clobbered.
 */
    random_number_seed[0] |= 1;
    randomization_request = NO;
}

uint32_t Crand(void)
{
/*
 * See Knuth vol 2 section 3.2.2 for a discussion of this random
 * number generator.
 */
    uint32_t temp;
    if (randomization_request) randomize();
    temp = (random_number_seed[random_k] += random_number_seed[random_j]);
    if (--random_j < 0) random_j = 54, --random_k;
    else if (--random_k < 0) random_k = 54;
    return temp;
}

void Csrand(uint32_t seed, uint32_t seed2)
{
/*
 * This allows you to put 64 bits of seed into the random sequence,
 * but it is very improbable that you have any good source of randomness
 * that good to start with! The input seeds are scrambled using md5
 * and then rather crudely widened to fill the whole array of seed data.
 * If the seed is specified as (0,0) then I will initialise things using
 * information from the time of day and the clock. This is NOT very
 * good, especially since I only use portable C-library ways of reading
 * the time. But it will at least not repeat for any single user and
 * since the clock information is then scrambled via md5 it will APPEAR
 * fairly unpredictable.
 */
    int i;
    unsigned char seedv[16], *p;
    random_j = 23;
    random_k = 54;
    i = 0;
    if (seed == 0 && seed2 == 0)
    {   randomization_request = YES;
        return;
    }
    randomization_request = NO;
/*
 * This version was byte-order sensitive, but documents the idea
 * that I first had.
 *    random_number_seed[0] = seed;
 *    random_number_seed[1] = 0x12345678;
 *    random_number_seed[2] = 0xa7086dee;
 *    random_number_seed[3] = seed2;
 * then I used the first 16 bytes of random_number_seed as input to md5.
 */
    seedv[0] = (seed & 0xff);
    seedv[1] = ((seed >> 8) & 0xff);
    seedv[2] = ((seed >> 16) & 0xff);
    seedv[3] = ((seed >> 24) & 0xff);
    seedv[4] = 0x78;
    seedv[5] = 0x56;
    seedv[6] = 0x34;
    seedv[7] = 0x12;
    seedv[8] = 0xee;
    seedv[9] = 0x6d;
    seedv[10] = 0x08;
    seedv[11] = 0xa7;
    seedv[12] = (seed2 & 0xff);
    seedv[13] = ((seed2 >> 8) & 0xff);
    seedv[14] = ((seed2 >> 16) & 0xff);
    seedv[15] = ((seed2 >> 24) & 0xff);
#ifdef TRACE_RANDOM
    for (i=0; i<16; i++) term_printf("%.2x ", seedv[i]);
    term_printf("\n");
#endif
/*
 * Next I will scramble the seed data that I have been given using md5
 * and place the resulting 128 bits of digested stuff in the start of
 * the seed vector.
 */
    CSL_MD5_Init();
    CSL_MD5_Update(seedv, 16);
    CSL_MD5_Final((unsigned char *)&random_number_seed[0]);
/*
 * The remainder of the vector gets filled using a simple linear
 * congruential scheme. Note that MD5 filled in BYTES andy what I need next
 * is an INTEGER, so to be byte-order insensitive I need to do things
 * the long way.
 */
    i = 4;
/*
 * Does anybody want to think about "strict alisasing" and the next little
 * fragment of code? Ha Ha.
 */
    p = (unsigned char *)random_number_seed;
    seed = p[0] | (p[1]<<8) | (p[2]<<16) | (p[3]<<24);
    random_number_seed[0] = seed;
    random_number_seed[1] = p[4] | (p[5]<<8) | (p[6]<<16) | (p[7]<<24);
    random_number_seed[2] = p[8] | (p[9]<<8) | (p[10]<<16) | (p[11]<<24);
    random_number_seed[3] = p[12] | (p[13]<<8) | (p[14]<<16) | (p[15]<<24);
    while (i<55)
    {   seed = 69069*seed + 1725307361;  /* computed modulo 2^32 */
        random_number_seed[i++] = seed;
    }
/*
 * I would like to make the least significant bits a little less
 * regular even to start with, so I xor in from one of the words that
 * md5 gave me.
 */
    seed = random_number_seed[1];
    i = 55-30;
    while (i<55)
    {   random_number_seed[i++] ^= seed & 1;
        seed = seed >> 1;
    }
/*
 * If all the least significant bits were zero to start with they would
 * always stay that way, so I force one of them to be 1.
 */
    random_number_seed[21] |= 1;
#ifdef TRACE_RANDOM
    for (i=0; i<55; i++) term_printf("%2d %.8x\n", i, random_number_seed[i]);
#endif
}

#ifdef COMMON
Lisp_Object Lrandom_2(Lisp_Object nil, Lisp_Object a, Lisp_Object bb)
{
    Lisp_Object b;
/*
 * Common Lisp expects an optional second arg to be used for the random
 * state - at present I do not support that, but it will not be too hard
 * when I get around to it...
 */
    b = bb;
    CSL_IGNORE(nil);
    if (is_fixnum(a))
    {   int32_t v = int_of_fixnum(a), p, q;
        if (v <= 0) return aerror1("random", a);
/* (random 1) always returns zero - a rather silly case! */
        else if (v == 1) return onevalue(fixnum_of_int(0));
/*
 * I generate a value that is an exact multiple of my range (v) and
 * pick random bitpatterns until I find one less than that.  On average
 * I will have only VERY slightly less than one draw needed, and doing things
 * this way ought to ensure that my pseudo random numbers are uniformly
 * distributed provided that the underlying generator is well behaved.
 */
        p = v*(0x7fffffff/v);
        do q = ((uint32_t)Crand()) >> 1; while (q > p);
        return onevalue(fixnum_of_int(q % v));
    }
    if (is_numbers(a))
    {   int32_t len, len1, msd;
        uint32_t w, w1;
        Lisp_Object r;
        if (!is_bignum(a)) return aerror1("random", a);
        len = bignum_length(a);
        push(a);
        r = getvector(TAG_NUMBERS, TYPE_BIGNUM, len);
        pop(a);
        errexit();
        len1 = (len-CELL)/4-1;
    restart:
        len = len1;
        msd = bignum_digits(a)[len];
        if (msd < 0) return aerror("negative arg for random"); /* -ve arg */
        if (msd == 0)
        {   bignum_digits(r)[len] = 0;
            len--;
            msd = bignum_digits(a)[len];
        }
        for (;;)
        {   w = (0xffffffffU/((uint32_t)msd+1U))*((uint32_t)msd+1U);
            do w1 = (uint32_t)Crand(); while (w1 >= w);
            w1 = w1%((uint32_t)msd+1U);
            bignum_digits(r)[len] = w1;
            if ((int32_t)w1 != msd) break;
/*
 * The loop to restart on the next line is when the random value I
 * have built up word by word ends up being equal to the input number - I
 * will discard it and start again in that case.
 */
            if (len == 0) goto restart;
            len--;
            msd = bignum_digits(a)[len];
        }
/*
 * having got some leading digits properly set up I can fill in the rest
 * as totally independent bit-patterns.
 */
        for (len--;len>=0; len--)
            bignum_digits(r)[len] = ((uint32_t)Crand())>>1;
        return onevalue(shrink_bignum(r, len1));
    }
    if (is_bfloat(a))
    {   Header h = flthdr(a);
        double d = float_of_number(a), v;
/*
 * The calculation here turns 62 bits of integer data into a floating
 * point number in the range 0.0 (inclusive) to 1.0 (exclusive).  Well,
 * to be more precise, rounding the value to the machine's floating point
 * format may round it up to be exactly 1.0, so I discard and cases where
 * that happens (once in several blue moons...).  If I wrote code that
 * knew exactly how many bits my floating point format had I could avoid
 * the need for that extra test, but it does not seem very painful to me
 * and I prefer the more portable code.
 */
        do
        {   v = ((double)(int32_t)(Crand() & 0x7fffffff)) / TWO_31;
            v += (double)(int32_t)(Crand() & 0x7fffffff);
            v /= TWO_31;
            v *= d;
        } while (v == d);
        a = make_boxfloat(v, type_of_header(h));
        errexit();
        return onevalue(a);
    }
    if (is_sfloat(a))
    {   Float_union d;
        float v;
        d.i = a - TAG_SFLOAT;
/*
 * similar idea to boxfloat case, but only 31 bits randomness used.
 * SOFTWARE_FLOATING_POINT conversion needed here, maybe
 */
        do
        {   v = (float)(int32_t)(Crand() & 0x7fffffff)/(float)TWO_31;
            v = v*d.f;
        } while (v == d.f);
        d.f = v;
        return onevalue((d.i & ~(int32_t)0xf) + TAG_SFLOAT);
    }
    return aerror1("random", a);
}
#endif

Lisp_Object Lrandom(Lisp_Object nil, Lisp_Object a)
{
    CSL_IGNORE(nil);
    if (is_fixnum(a))
    {   int32_t v = int_of_fixnum(a), p, q;
        if (v <= 0) return aerror1("random", a);
/* (random 1) always returns zero - a rather silly case! */
        else if (v == 1) return onevalue(fixnum_of_int(0));
/*
 * I generate a value that is an exact multiple of my range (v) and
 * pick random bitpatterns until I find one less than that.  On average
 * I will have only VERY slightly less than one draw needed, and doing things
 * this way ought to ensure that my pseudo random numbers are uniformly
 * distributed provided that the underlying generator is well behaved.
 */
        p = v*(0x7fffffff/v);
        do q = ((uint32_t)Crand()) >> 1; while (q > p);
        return onevalue(fixnum_of_int(q % v));
    }
    if (is_numbers(a))
    {   int32_t len, len1, msd;
        uint32_t w, w1;
        Lisp_Object r;
        if (!is_bignum(a)) return aerror1("random", a);
        len = bignum_length(a);
        push(a);
        r = getvector(TAG_NUMBERS, TYPE_BIGNUM, len);
        pop(a);
        errexit();
        len1 = (len-CELL)/4-1;
    restart:
        len = len1;
        msd = bignum_digits(a)[len];
        if (msd < 0) return aerror("negative arg for random"); /* -ve arg */
        if (msd == 0)
        {   bignum_digits(r)[len] = 0;
            len--;
            msd = bignum_digits(a)[len];
        }
        for (;;)
        {   w = (0xffffffffU/((uint32_t)msd+1U))*((uint32_t)msd+1U);
            do w1 = (uint32_t)Crand(); while (w1 >= w);
            w1 = w1%((uint32_t)msd+1U);
            bignum_digits(r)[len] = w1;
            if ((int32_t)w1 != msd) break;
/*
 * The loop to restart on the next line is when the random value I
 * have built up word by word ends up being equal to the input number - I
 * will discard it and start again in that case.
 */
            if (len == 0) goto restart;
            len--;
            msd = bignum_digits(a)[len];
        }
/*
 * having got some leading digits properly set up I can fill in the rest
 * as totally independent bit-patterns.
 */
        for (len--;len>=0; len--)
            bignum_digits(r)[len] = ((uint32_t)Crand())>>1;
        return onevalue(shrink_bignum(r, len1));
    }
    if (is_bfloat(a))
    {   Header h = flthdr(a);
        double d = float_of_number(a), v;
/*
 * The calculation here turns 62 bits of integer data into a floating
 * point number in the range 0.0 (inclusive) to 1.0 (exclusive).  Well,
 * to be more precise, rounding the value to the machine's floating point
 * format may round it up to be exactly 1.0, so I discard and cases where
 * that happens (once in several blue moons...).  If I wrote code that
 * knew exactly how many bits my floating point format had I could avoid
 * the need for that extra test, but it does not seem very painful to me
 * and I prefer the more portable code.
 */
        do
        {   v = ((double)(int32_t)(Crand() & 0x7fffffff)) / TWO_31;
            v += (double)(int32_t)(Crand() & 0x7fffffff);
            v /= TWO_31;
            v *= d;
        } while (v == d);
        a = make_boxfloat(v, type_of_header(h));
        errexit();
        return onevalue(a);
    }
#ifdef COMMON
    if (is_sfloat(a))
    {   Float_union d;
        float v;
        d.i = a - TAG_SFLOAT;
/*
 * similar idea to boxfloat case, but only 31 bits randomness used.
 * SOFTWARE_FLOATING_POINT conversion needed here, maybe
 */
        do
        {   v = (float)(int32_t)(Crand() & 0x7fffffff)/(float)TWO_31;
            v = v*d.f;
        } while (v == d.f);
        d.f = v;
        return onevalue((d.i & ~(int32_t)0xf) + TAG_SFLOAT);
    }
#endif
    return aerror1("random", a);
}

Lisp_Object MS_CDECL Lnext_random(Lisp_Object nil, int nargs, ...)
/*
 * Returns a random positive fixnum.  27 bits in this Lisp!
 */
{
    int32_t r;
    argcheck(nargs, 0, "next-random");
    CSL_IGNORE(nil);
    r = Crand();
    return onevalue((Lisp_Object)((r & 0x7ffffff0) + TAG_FIXNUM));
}

Lisp_Object Lmake_random_state(Lisp_Object nil, Lisp_Object a, Lisp_Object b)
{
/*
 * Nasty temporary hack here to allow me to set the seed for the
 * random number generator in Standard Lisp mode.  I need to re-think
 * this soon before it feels frozen in! Oops - too late!!!
 */
    CSL_IGNORE(b);
    if (!is_fixnum(a)) return aerror1("make-random-state", a);
    Csrand(int_of_fixnum(a),
           is_fixnum(b) ? int_of_fixnum(b) : 0);
    return onevalue(nil);
}

Lisp_Object Lmake_random_state1(Lisp_Object nil, Lisp_Object a)
{
    if (!is_fixnum(a)) return aerror1("make-random-state", a);
    Csrand(int_of_fixnum(a), 0);
    return onevalue(nil);
}

/*
 * The function md5() can be given a number or a string as an argument,
 * and it uses the md5 message digest algorithm to reduce it to a
 * numeric value in the range 0 to 2^128.
 * Well actually I will also allow an arbitrary expression, which I
 * will treat as if it has to be printed...
 */

Lisp_Object Lmd5(Lisp_Object env, Lisp_Object a)
{
    Lisp_Object nil = C_nil;
    Lisp_Object r;
    unsigned char md[16];
    uint32_t v0, v1, v2, v3, v4;
    int32_t len, i;
    CSL_IGNORE(env);
    if (is_fixnum(a))
    {   sprintf((char *)md, "%.8lx", (unsigned long)a);
        CSL_MD5_Init();
        CSL_MD5_Update(md, 8);
    }
    else if (is_numbers(a) && is_bignum_header(numhdr(a)))
    {   len = length_of_header(numhdr(a));
        CSL_MD5_Init();
        for (i=CELL; i<len; i+=4)
        {   sprintf((char *)md, "%.8lx", (unsigned long)bignum_digits(a)[(i-CELL)/4]);
            CSL_MD5_Update(md, 8);
        }
    }
    else if (is_vector(a) && type_of_header(vechdr(a)) == TYPE_STRING)
    {   len = length_of_header(vechdr(a));
        CSL_MD5_Init();
        CSL_MD5_Update((unsigned char *)(a + CELL - TAG_VECTOR), len-CELL);
    }
    else checksum(a);
    CSL_MD5_Final(md);
    v0 = md[0] + (md[1]<<8) + (md[2]<<16) + (md[3]<<24);
    v1 = md[4] + (md[5]<<8) + (md[6]<<16) + (md[7]<<24);
    v2 = md[8] + (md[9]<<8) + (md[10]<<16) + (md[11]<<24);
    v3 = md[12] + (md[13]<<8) + (md[14]<<16) + (md[15]<<24);
    v4 = v3 >> 28;
    v3 = ((v3 << 3) | (v2 >> 29)) & 0x7fffffff;
    v2 = ((v2 << 2) | (v1 >> 30)) & 0x7fffffff;
    v1 = ((v1 << 1) | (v0 >> 31)) & 0x7fffffff;
    v0 &= 0x7fffffff;
/*
 * Note the funny tests. This is because in my representation the
 * top word of a bignum is a 2s complement signed value and to keep clear
 * of overflow that means I use an extra digit slightly before one might
 * imagine it is necessary!
 */
    if (v4 != 0 || (v3 & 0x40000000) != 0) len = CELL+20;
    else if (v3 != 0 || (v2 & 0x40000000) != 0) len = CELL+16;
    else if (v2 != 0 || (v1 & 0x40000000) != 0) len = CELL+12;
    else if (v1 != 0 || (v0 & 0x40000000) != 0) len = CELL+8;
    else if ((v0 & fix_mask) != 0) len = CELL+4;
    else return onevalue(fixnum_of_int(v0));
    r = getvector(TAG_NUMBERS, TYPE_BIGNUM, len);
    errexit();
    if (SIXTY_FOUR_BIT)
    {   switch (len)
        {
    case CELL+20:
            bignum_digits(r)[5] = 0;  /* zeros out padding word as necessary */
            bignum_digits(r)[4] = v4;
    case CELL+16:
    case CELL+12:
            bignum_digits(r)[3] = v3;
            bignum_digits(r)[2] = v2;
    case CELL+8:
    case CELL+4:
            bignum_digits(r)[1] = v1;
            bignum_digits(r)[0] = v0;
            break;
        }
    }
    else
    {   switch (len)
        {
    case CELL+20:
    case CELL+16:
            bignum_digits(r)[4] = v4; /* zeros out padding word as necessary */
            bignum_digits(r)[3] = v3;
    case CELL+12:
    case CELL+8:
            bignum_digits(r)[2] = v2;
            bignum_digits(r)[1] = v1;
    case CELL+4:
            bignum_digits(r)[0] = v0;
            break;
        }
    }
/*  validate_number("MD5", r, r, r); */
    return onevalue(r);
}

/*
 * md60 is a function that uses MD5 but then returns just about 60 bits
 * of number not 128. It is for use when the full 128 bits of checksum
 * would be clumsy overkill.
 */

Lisp_Object Lmd60(Lisp_Object env, Lisp_Object a)
{
    Lisp_Object nil = C_nil;
    Lisp_Object r;
    unsigned char md[16];
    uint32_t v0, v1;
    int32_t len, i;
    CSL_IGNORE(env);
    if (is_fixnum(a))
    {   sprintf((char *)md, "%.8lx", (unsigned long)a);
        CSL_MD5_Init();
        CSL_MD5_Update(md, 8);
    }
    else if (is_numbers(a) && is_bignum_header(numhdr(a)))
    {   len = length_of_header(numhdr(a));
        CSL_MD5_Init();
        for (i=CELL; i<len; i+=4)
        {   sprintf((char *)md, "%.8lx", (unsigned long)bignum_digits(a)[(i-CELL)/4]);
            CSL_MD5_Update(md, 8);
        }
    }
    else if (is_vector(a) && type_of_header(vechdr(a)) == TYPE_STRING)
    {   len = length_of_header(vechdr(a));
        CSL_MD5_Init();
        CSL_MD5_Update((unsigned char *)(a + CELL - TAG_VECTOR), len-CELL);
    }
    else checksum(a);
    CSL_MD5_Final(md);
    v0 = md[0] + (md[1]<<8) + (md[2]<<16) + (md[3]<<24);
    v1 = md[4] + (md[5]<<8) + (md[6]<<16) + (md[7]<<24);
    v1 = ((v1 << 1) | (v0 >> 31)) & 0x3fffffff;
    v0 &= 0x7fffffff;
    if (v1 != 0 || (v0 & 0x40000000) != 0) len = CELL+8;
#ifdef PERMIT_SHORT_CHECKSUMS
    else if ((v0 & fix_mask) != 0) len = CELL+4;
    else return onevalue(fixnum_of_int(v0));
#else
    else
    {
/*
 * Here I ensure that the checksum that I return is a 2-word bignum.
 * This SKEWS the distribution somewhat, in that results lower than 2^30
 * will never be returned. In the very unusual case that the low 61 bits
 * of md5 were all zero I return a somewhat arbitrary alternative value.
 */
        if (v0 != 0)
        {   v1 = v0;
            v0 = md[8] + (md[9]<<8) + (md[10]<<16) + (md[11]<<24);
            v0 &= 0x7fffffff;
            len = CELL+8;
        }
        else
        {   v1 = 0x12345678;
            len = CELL+8;
        }
    }
#endif
    r = getvector(TAG_NUMBERS, TYPE_BIGNUM, len);
    errexit();
    if (SIXTY_FOUR_BIT)
    {   bignum_digits(r)[1] = v1;
        bignum_digits(r)[0] = v0;
    }
    else
    {   switch (len)
        {
    case CELL+8:
            bignum_digits(r)[2] = 0;
            bignum_digits(r)[1] = v1;
    case CELL+4:
            bignum_digits(r)[0] = v0;
            break;
        }
    }
/*  validate_number("MD60", r, r, r); */
    return onevalue(r);
}

static Lisp_Object Llogand2(Lisp_Object env, Lisp_Object a1, Lisp_Object a2)
{
    return Lboolfn(env, 2, a1, a2);
}

static Lisp_Object Llogeqv2(Lisp_Object env, Lisp_Object a1, Lisp_Object a2)
{
    return Lboolfn(env, 2, a1, a2);
}

static Lisp_Object Llogxor2(Lisp_Object env, Lisp_Object a1, Lisp_Object a2)
{
    return Lboolfn(env, 2, a1, a2);
}

static Lisp_Object Llogor2(Lisp_Object env, Lisp_Object a1, Lisp_Object a2)
{
    return Lboolfn(env, 2, a1, a2);
}

setup_type const arith06_setup[] =
{
    {"ash",                     too_few_2, Lash, wrong_no_2},
    {"ash1",                    too_few_2, Lash1, wrong_no_2},
    {"divide",                  too_few_2, Ldivide, wrong_no_2},
    {"evenp",                   Levenp, too_many_1, wrong_no_1},
    {"inorm",                   too_few_2, Linorm, wrong_no_2},
    {"logand",                  Lidentity, Llogand2, Lboolfn},
    {"logeqv",                  Lidentity, Llogeqv2, Lboolfn},
    {"lognot",                  Llognot, too_many_1, wrong_no_1},
    {"logxor",                  Lidentity, Llogxor2, Lboolfn},
    {"lsd",                     Llsd, too_many_1, wrong_no_1},
    {"make-random-state",       Lmake_random_state1, Lmake_random_state, wrong_no_2},
    {"max",                     Lidentity, Lmax2, Lmax},
    {"max2",                    too_few_2, Lmax2, wrong_no_2},
    {"min",                     Lidentity, Lmin2, Lmin},
    {"min2",                    too_few_2, Lmin2, wrong_no_2},
    {"minus",                   Lminus, too_many_1, wrong_no_1},
    {"minusp",                  Lminusp, too_many_1, wrong_no_1},
    {"mod",                     too_few_2, Lmod, wrong_no_2},
    {"msd",                     Lmsd, too_many_1, wrong_no_1},
    {"oddp",                    Loddp, too_many_1, wrong_no_1},
    {"onep",                    Lonep, too_many_1, wrong_no_1},
    {"plus2",                   too_few_2, Lplus2, wrong_no_2},
    {"plusp",                   Lplusp, too_many_1, wrong_no_1},
    {"rational",                Lrational, too_many_1, wrong_no_1},
    {"times2",                  too_few_2, Ltimes2, wrong_no_2},
    {"zerop",                   Lzerop, too_many_1, wrong_no_1},
    {"md5",                     Lmd5, too_many_1, wrong_no_1},
    {"md60",                    Lmd60, too_many_1, wrong_no_1},
#ifdef COMMON
    {"*",                       Lidentity, Ltimes2, Ltimes},
    {"+",                       Lidentity, Lplus2, Lplus},
    {"-",                       Lminus, Ldifference2, Ldifference},
    {"/",                       Lquotient_1, Lquotient, Lquotient_n},
    {"/=",                      Lneq_1, Lneq_2, Lneqn},
    {"1+",                      Ladd1, too_many_1, wrong_no_1},
    {"1-",                      Lsub1, too_many_1, wrong_no_1},
    {"<",                       Llessp_1, Llessp, Llessp_n},
    {"<=",                      Lleq_1, Lleq, Lleq_n},
    {"=",                       Leqn_1, Leqn, Leqn_n},
    {">",                       Lgreaterp_1, Lgreaterp, Lgreaterp_n},
    {">=",                      Lgeq_1, Lgeq, Lgeq_n},
    {"float",                   Lfloat, Lfloat_2, wrong_no_1},
    {"logior",                  Lidentity, Llogor2, Lboolfn},
    {"random",                  Lrandom, Lrandom_2, wrong_no_1},
    {"rationalize",             Lrationalize, too_many_1, wrong_no_1},
    {"manexp",                  Lmanexp, too_many_1, wrong_no_1},
    {"rem",                     too_few_2, Lrem, wrong_no_2},
/*
 * I also provide the old style names to make porting code easier for me
 */
    {"times",                   Lidentity, Ltimes2, Ltimes},
    {"plus",                    Lidentity, Lplus2, Lplus},
    {"times2",                  too_few_2, Ltimes2, wrong_no_2},
    {"plus2",                   too_few_2, Lplus2, wrong_no_2},
    {"minus",                   Lminus, too_many_1, wrong_no_1},
    {"difference",              too_few_2, Ldifference2, Ldifference},
/* I leave QUOTIENT as the integer-truncating form, while "/" gives ratios */
    {"quotient",                too_few_2, LSLquotient, wrong_no_2},
    {"remainder",               too_few_2, Lrem, wrong_no_2},
    {"add1",                    Ladd1, too_many_1, wrong_no_1},
    {"sub1",                    Lsub1, too_many_1, wrong_no_1},
    {"lessp",                   Llessp_1, Llessp, Llessp_n},
    {"leq",                     Lleq_1, Lleq, Lleq_n},
    {"eqn",                     Leqn_1, Leqn, Leqn_n},
    {"greaterp",                Lgreaterp_1, Lgreaterp, Lgreaterp_n},
    {"geq",                     Lgeq_1, Lgeq, Lgeq_n},
    {"next-random-number",      wrong_no_0a, wrong_no_0b, Lnext_random},
    {"logor",                   Lidentity, Llogor2, Lboolfn},
#else
    {"add1",                    Ladd1, too_many_1, wrong_no_1},
    {"difference",              too_few_2, Ldifference2, wrong_no_2},
    {"eqn",                     too_few_2, Leqn, wrong_no_2},
    {"float",                   Lfloat, too_many_1, wrong_no_1},
    {"geq",                     too_few_2, Lgeq, wrong_no_2},
    {"greaterp",                too_few_2, Lgreaterp, wrong_no_2},
    {"leq",                     too_few_2, Lleq, wrong_no_2},
    {"lessp",                   too_few_2, Llessp, wrong_no_2},
    {"logor",                   Lidentity, Llogor2, Lboolfn},
    {"quotient",                too_few_2, Lquotient, wrong_no_2},
/*
 * I used to call these just random and next-random-number, but REDUCE
 * wants its own versions of those (for cross-Lisp consistency) so I use
 * alternative names here.
 */
    {"random-number",           Lrandom, too_many_1, wrong_no_1},
    {"random-fixnum",           wrong_no_0a, wrong_no_0b, Lnext_random},
    {"remainder",               too_few_2, Lrem, wrong_no_2},
    {"sub1",                    Lsub1, too_many_1, wrong_no_1},
#endif
    {NULL,                      0, 0, 0}
};

/* end of arith06.c */