[bpt/guile.git] / libguile / numbers.c

/*      Copyright (C) 1995,1996,1997,1998, 1999 Free Software Foundation, Inc.

 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2, or (at your option)
 * any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this software; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
 * Boston, MA 02111-1307 USA
 *
 * As a special exception, the Free Software Foundation gives permission
 * for additional uses of the text contained in its release of GUILE.
 *
 * The exception is that, if you link the GUILE library with other files
 * to produce an executable, this does not by itself cause the
 * resulting executable to be covered by the GNU General Public License.
 * Your use of that executable is in no way restricted on account of
 * linking the GUILE library code into it.
 *
 * This exception does not however invalidate any other reasons why
 * the executable file might be covered by the GNU General Public License.
 *
 * This exception applies only to the code released by the
 * Free Software Foundation under the name GUILE.  If you copy
 * code from other Free Software Foundation releases into a copy of
 * GUILE, as the General Public License permits, the exception does
 * not apply to the code that you add in this way.  To avoid misleading
 * anyone as to the status of such modified files, you must delete
 * this exception notice from them.
 *
 * If you write modifications of your own for GUILE, it is your choice
 * whether to permit this exception to apply to your modifications.
 * If you do not wish that, delete this exception notice.  */

/* Software engineering face-lift by Greg J. Badros, 11-Dec-1999,
   gjb@cs.washington.edu, http://www.cs.washington.edu/homes/gjb */

\f

#include <stdio.h>
#include <math.h>
#include "_scm.h"
#include "genio.h"
#include "unif.h"
#include "feature.h"
#include "smob.h"

#include "scm_validate.h"
#include "numbers.h"
\f
#define DIGITS '0':case '1':case '2':case '3':case '4':\
 case '5':case '6':case '7':case '8':case '9'


/* IS_INF tests its floating point number for infiniteness
 */
#ifndef IS_INF
#define IS_INF(x) ((x) == (x) / 2)
#endif

/* Return true if X is not infinite and is not a NaN
 */
#ifndef isfinite
#define isfinite(x) (!IS_INF (x) && (x) == (x))
#endif

/* MAXEXP is the maximum double precision expontent
 * FLTMAX is less than or scm_equal the largest single precision float
 */

#ifdef SCM_FLOATS
#ifdef STDC_HEADERS
#ifndef GO32
#include <float.h>
#endif /* ndef GO32 */
#endif /* def STDC_HEADERS */
#ifdef DBL_MAX_10_EXP
#define MAXEXP DBL_MAX_10_EXP
#else
#define MAXEXP 308		/* IEEE doubles */
#endif /* def DBL_MAX_10_EXP */
#ifdef FLT_MAX
#define FLTMAX FLT_MAX
#else
#define FLTMAX 1e+23
#endif /* def FLT_MAX */
#endif /* def SCM_FLOATS */
\f


SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, 
            (SCM x),
	    "")
#define FUNC_NAME s_scm_exact_p
{
  if (SCM_INUMP (x))
    return SCM_BOOL_T;
#ifdef SCM_BIGDIG
  if (SCM_BIGP (x))
    return SCM_BOOL_T;
#endif
  return SCM_BOOL_F;
}
#undef FUNC_NAME

SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, 
            (SCM n),
	    "")
#define FUNC_NAME s_scm_odd_p
{
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (n))
    {
      SCM_VALIDATE_BIGINT (1,n);
      return SCM_BOOL(1 & SCM_BDIGITS (n)[0]);
    }
#else
  SCM_VALIDATE_INUM (1,n);
#endif
  return SCM_BOOL(4 & (int) n);
}
#undef FUNC_NAME

SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, 
            (SCM n),
	    "")
#define FUNC_NAME s_scm_even_p
{
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (n))
    {
      SCM_VALIDATE_BIGINT (1,n);
      return SCM_NEGATE_BOOL(1 & SCM_BDIGITS (n)[0]);
    }
#else
  SCM_VALIDATE_INUM (1,n);
#endif
  return SCM_NEGATE_BOOL(4 & (int) n);
}
#undef FUNC_NAME

SCM_GPROC (s_abs, "abs", 1, 0, 0, scm_abs, g_abs);

SCM
scm_abs (SCM x)
{
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT1 (SCM_BIGP (x), g_abs, x, SCM_ARG1, s_abs);
      if (SCM_TYP16 (x) == scm_tc16_bigpos)
	return x;
      return scm_copybig (x, 0);
    }
#else
  SCM_GASSERT1 (SCM_INUMP (x), g_abs, x, SCM_ARG1, s_abs);
#endif
  if (SCM_INUM (x) >= 0)
    return x;
  x = - SCM_INUM (x);
  if (!SCM_POSFIXABLE (x))
#ifdef SCM_BIGDIG
    return scm_long2big (x);
#else
  scm_num_overflow (s_abs);
#endif
  return SCM_MAKINUM (x);
}

SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient);

SCM
scm_quotient (SCM x, SCM y)
{
  register long z;
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      long w;
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_quotient, x, y, SCM_ARG1, s_quotient);
      if (SCM_NINUMP (y))
	{
	  SCM_ASRTGO (SCM_BIGP (y), bady);
	  return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				SCM_BDIGITS (y), SCM_NUMDIGS (y),
				SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 2);
	}
      z = SCM_INUM (y);
      SCM_ASRTGO (z, ov);
      if (1 == z)
	return x;
      if (z < 0)
	z = -z;
      if (z < SCM_BIGRAD)
	{
	  w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0));
	  scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), (SCM_BIGDIG) z);
	  return scm_normbig (w);
	}
#ifndef SCM_DIGSTOOBIG
      w = scm_pseudolong (z);
      return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			    (SCM_BIGDIG *) & w, SCM_DIGSPERLONG,
			    SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 2);
#else
      {
	SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	scm_longdigs (z, zdigs);
	return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			      zdigs, SCM_DIGSPERLONG,
			      SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 2);
      }
#endif
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
	}
      return SCM_INUM0;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_quotient, x, y, SCM_ARG1, s_quotient);
  SCM_GASSERT2 (SCM_INUMP (y), g_quotient, x, y, SCM_ARG2, s_quotient);
#endif
  if ((z = SCM_INUM (y)) == 0)
    {
    ov:
      scm_num_overflow (s_quotient);
    }
  z = SCM_INUM (x) / z;
#ifdef BADIVSGNS
  {
#if (__TURBOC__ == 1)
    long t = ((y < 0) ? -SCM_INUM (x) : SCM_INUM (x)) % SCM_INUM (y);
#else
    long t = SCM_INUM (x) % SCM_INUM (y);
#endif
    if (t == 0);
    else if (t < 0)
      if (x < 0);
      else
	z--;
    else if (x < 0)
      z++;
  }
#endif
  if (!SCM_FIXABLE (z))
#ifdef SCM_BIGDIG
    return scm_long2big (z);
#else
  scm_num_overflow (s_quotient);
#endif
  return SCM_MAKINUM (z);
}

SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder);

SCM
scm_remainder (SCM x, SCM y)
{
  register long z;
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_remainder, x, y, SCM_ARG1, s_remainder);
      if (SCM_NINUMP (y))
	{
	  SCM_ASRTGO (SCM_BIGP (y), bady);
	  return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				SCM_BDIGITS (y), SCM_NUMDIGS (y),
				SCM_BIGSIGN (x), 0);
	}
      if (!(z = SCM_INUM (y)))
	goto ov;
      return scm_divbigint (x, z, SCM_BIGSIGN (x), 0);
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
	}
      return x;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_remainder, x, y, SCM_ARG1, s_remainder);
  SCM_GASSERT2 (SCM_INUMP (y), g_remainder, x, y, SCM_ARG2, s_remainder);
#endif
  if (!(z = SCM_INUM (y)))
    {
    ov:
      scm_num_overflow (s_remainder);
    }
#if (__TURBOC__ == 1)
  if (z < 0)
    z = -z;
#endif
  z = SCM_INUM (x) % z;
#ifdef BADIVSGNS
  if (!z);
  else if (z < 0)
    if (x < 0);
    else
      z += SCM_INUM (y);
  else if (x < 0)
    z -= SCM_INUM (y);
#endif
  return SCM_MAKINUM (z);
}

SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo);

SCM
scm_modulo (SCM x, SCM y)
{
  register long yy, z;
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_modulo, x, y, SCM_ARG1, s_modulo);
      if (SCM_NINUMP (y))
	{
	  SCM_ASRTGO (SCM_BIGP (y), bady);
	  return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				SCM_BDIGITS (y), SCM_NUMDIGS (y),
				SCM_BIGSIGN (y),
				(SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)) ? 1 : 0);
	}
      if (!(z = SCM_INUM (y)))
	goto ov;
      return scm_divbigint (x, z, y < 0,
			    (SCM_BIGSIGN (x) ? (y > 0) : (y < 0)) ? 1 : 0);
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
	}
      return (SCM_BIGSIGN (y) ? (x > 0) : (x < 0)) ? scm_sum (x, y) : x;
    }
#else
  SCM_GASSERT1 (SCM_INUMP (x), g_modulo, x, y, SCM_ARG1, s_modulo);
  SCM_GASSERT2 (SCM_INUMP (y), g_modulo, x, y, SCM_ARG2, s_modulo);
#endif
  if (!(yy = SCM_INUM (y)))
    {
    ov:
      scm_num_overflow (s_modulo);
    }
#if (__TURBOC__==1)
  z = SCM_INUM (x);
  z = ((yy < 0) ? -z : z) % yy;
#else
  z = SCM_INUM (x) % yy;
#endif
  return SCM_MAKINUM (((yy < 0) ? (z > 0) : (z < 0)) ? z + yy : z);
}

SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd);

SCM
scm_gcd (SCM x, SCM y)
{
  register long u, v, k, t;
  if (SCM_UNBNDP (y))
    return SCM_UNBNDP (x) ? SCM_INUM0 : x;
 tailrec:
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
    big_gcd:
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_gcd, x, y, SCM_ARG1, s_gcd);
      if (SCM_BIGSIGN (x))
	x = scm_copybig (x, 0);
    newy:
      if (SCM_NINUMP (y))
	{
	  SCM_GASSERT2 (SCM_BIGP (y),
			g_gcd, x, y, SCM_ARGn, s_gcd);
	  if (SCM_BIGSIGN (y))
	    y = scm_copybig (y, 0);
	  switch (scm_bigcomp (x, y))
	    {
	    case -1:
	    swaprec:
	    t = scm_remainder (x, y);
	    x = y;
	    y = t;
	    goto tailrec;
	    case 0:
	      return x;
	    case 1:
	      y = scm_remainder (y, x);
	      goto newy;
	    }
	  /* instead of the switch, we could just
	     return scm_gcd (y, scm_modulo (x, y)); */
	}
      if (SCM_INUM0 == y)
	return x;
      goto swaprec;
    }
  if (SCM_NINUMP (y))
    {
      t = x;
      x = y;
      y = t;
      goto big_gcd;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_gcd, x, y, SCM_ARG1, s_gcd);
  SCM_GASSERT2 (SCM_INUMP (y), g_gcd, x, y, SCM_ARGn, s_gcd);
#endif
  u = SCM_INUM (x);
  if (u < 0)
    u = -u;
  v = SCM_INUM (y);
  if (v < 0)
    v = -v;
  else if (0 == v)
    goto getout;
  if (0 == u)
    {
      u = v;
      goto getout;
    }
  for (k = 1; !(1 & ((int) u | (int) v)); k <<= 1, u >>= 1, v >>= 1);
  if (1 & (int) u)
    t = -v;
  else
    {
      t = u;
    b3:
      t = SCM_SRS (t, 1);
    }
  if (!(1 & (int) t))
    goto b3;
  if (t > 0)
    u = t;
  else
    v = -t;
  if ((t = u - v))
    goto b3;
  u = u * k;
 getout:
  if (!SCM_POSFIXABLE (u))
#ifdef SCM_BIGDIG
    return scm_long2big (u);
#else
  scm_num_overflow (s_gcd);
#endif
  return SCM_MAKINUM (u);
}

SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm);

SCM
scm_lcm (SCM n1, SCM n2)
{
  SCM d;
#ifndef SCM_BIGDIG
  SCM_GASSERT2 (SCM_INUMP (n1) || SCM_UNBNDP (n1),
		g_lcm, n1, n2, SCM_ARG1, s_lcm);
  SCM_GASSERT2 (SCM_INUMP (n2) || SCM_UNBNDP (n2),
		g_lcm, n1, n2, SCM_ARGn, s_lcm);
#else
  SCM_GASSERT2 (SCM_INUMP (n1)
		|| SCM_UNBNDP (n1)
		|| (SCM_BIGP (n1)),
		g_lcm, n1, n2, SCM_ARG1, s_lcm);
  SCM_GASSERT2 (SCM_INUMP (n2)
		|| SCM_UNBNDP (n2)
		|| (SCM_BIGP (n2)),
		g_lcm, n1, n2, SCM_ARGn, s_lcm);
#endif
  if (SCM_UNBNDP (n2))
    {
      n2 = SCM_MAKINUM (1L);
      if (SCM_UNBNDP (n1))
	return n2;
    }
  
  d = scm_gcd (n1, n2);
  if (SCM_INUM0 == d)
    return d;
  return scm_abs (scm_product (n1, scm_quotient (n2, d)));
}

#ifndef SCM_BIGDIG
#ifndef SCM_FLOATS
#define scm_long2num SCM_MAKINUM
#endif
#endif

#ifndef scm_long2num
#define SCM_LOGOP_RETURN(x) scm_ulong2num(x)
#else
#define SCM_LOGOP_RETURN(x) SCM_MAKINUM(x)
#endif

SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr,
             (SCM n1, SCM n2),
	     "Returns the integer which is the bit-wise AND of the two integer\n"
	     "arguments.\n\n"
	     "Example:\n"
	     "@lisp\n"
	     "(number->string (logand #b1100 #b1010) 2)\n"
	     "   @result{} \"1000\"")
#define FUNC_NAME s_scm_logand
{
  int i1, i2;
  if (SCM_UNBNDP (n2))
    {
      if (SCM_UNBNDP (n1))
	return SCM_MAKINUM (-1);
      return n1;
    }
  SCM_VALIDATE_ULONG_COPY (1,n1,i1);
  SCM_VALIDATE_ULONG_COPY (2,n2,i2);
  return SCM_LOGOP_RETURN (i1 & i2);
}
#undef FUNC_NAME

SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr,
             (SCM n1, SCM n2),
	     "Returns the integer which is the bit-wise OR of the two integer\n"
	     "arguments.\n\n"
	     "Example:\n"
	     "@lisp\n"
	     "(number->string (logior #b1100 #b1010) 2)\n"
	     "   @result{} \"1110\"\n"
	     "@end lisp")
#define FUNC_NAME s_scm_logior
{
  int i1, i2;
  if (SCM_UNBNDP (n2))
    {
      if (SCM_UNBNDP (n1))
	return SCM_INUM0;
      return n1;
    }
  SCM_VALIDATE_ULONG_COPY (1,n1,i1);
  SCM_VALIDATE_ULONG_COPY (2,n2,i2);
  return SCM_LOGOP_RETURN (i1 | i2);
}
#undef FUNC_NAME

SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr,
             (SCM n1, SCM n2),
	     "Returns the integer which is the bit-wise XOR of the two integer\n"
	     "arguments.\n\n"
	     "Example:\n"
	     "@lisp\n"
	     "(number->string (logxor #b1100 #b1010) 2)\n"
	     "   @result{} \"110\"\n"
	     "@end lisp")
#define FUNC_NAME s_scm_logxor
{
  int i1, i2;
  if (SCM_UNBNDP (n2))
    {
      if (SCM_UNBNDP (n1))
	return SCM_INUM0;
      return n1;
    }
  SCM_VALIDATE_ULONG_COPY (1,n1,i1);
  SCM_VALIDATE_ULONG_COPY (2,n2,i2);
  return SCM_LOGOP_RETURN (i1 ^ i2);
}
#undef FUNC_NAME

SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0,
            (SCM n1, SCM n2),
	    "@example\n"
	    "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n"
	    "(logtest #b0100 #b1011) @result{} #f\n"
	    "(logtest #b0100 #b0111) @result{} #t\n"
	    "@end example")
#define FUNC_NAME s_scm_logtest
{
  int i1, i2;
  SCM_VALIDATE_ULONG_COPY (1,n1,i1);
  SCM_VALIDATE_ULONG_COPY (2,n2,i2);
  return SCM_BOOL(i1 & i2);
}
#undef FUNC_NAME


SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0,
            (SCM index, SCM j),
	    "@example\n"
	    "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n"
	    "(logbit? 0 #b1101) @result{} #t\n"
	    "(logbit? 1 #b1101) @result{} #f\n"
	    "(logbit? 2 #b1101) @result{} #t\n"
	    "(logbit? 3 #b1101) @result{} #t\n"
	    "(logbit? 4 #b1101) @result{} #f\n"
	    "@end example")
#define FUNC_NAME s_scm_logbit_p
{
  int i1, i2;
  SCM_VALIDATE_INUM_MIN_COPY (1,index,0,i1);
  SCM_VALIDATE_ULONG_COPY (2,j,i2);
  return SCM_BOOL((1 << i1) & i2);
}
#undef FUNC_NAME

SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, 
            (SCM n),
	    "Returns the integer which is the 2s-complement of the integer argument.\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(number->string (lognot #b10000000) 2)\n"
	    "   @result{} \"-10000001\"\n"
	    "(number->string (lognot #b0) 2)\n"
	    "   @result{} \"-1\"\n"
	    "@end lisp\n"
	    "")
#define FUNC_NAME s_scm_lognot
{
  SCM_VALIDATE_INUM (1,n);
  return scm_difference (SCM_MAKINUM (-1L), n);
}
#undef FUNC_NAME

SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0,
            (SCM n, SCM k),
	    "Returns @var{n} raised to the non-negative integer exponent @var{k}.\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(integer-expt 2 5)\n"
	    "   @result{} 32\n"
	    "(integer-expt -3 3)\n"
	    "   @result{} -27\n"
	    "@end lisp")
#define FUNC_NAME s_scm_integer_expt
{
  SCM acc = SCM_MAKINUM (1L);
  int i2;
#ifdef SCM_BIGDIG
  if (SCM_INUM0 == n || acc == n)
    return n;
  else if (SCM_MAKINUM (-1L) == n)
    return SCM_BOOL_F == scm_even_p (k) ? n : acc;
#endif
  SCM_VALIDATE_ULONG_COPY (2,k,i2);
  if (i2 < 0)
    {
      i2 = -i2;
      n = scm_divide (n, SCM_UNDEFINED);
    }
  while (1)
    {
      if (0 == i2)
	return acc;
      if (1 == i2)
	return scm_product (acc, n);
      if (i2 & 1)
	acc = scm_product (acc, n);
      n = scm_product (n, n);
      i2 >>= 1;
    }
}
#undef FUNC_NAME

SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
            (SCM n, SCM cnt),
	    "Returns an integer equivalent to\n"
	    "@code{(inexact->exact (floor (* @var{int} (expt 2 @var{count}))))}.@refill\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(number->string (ash #b1 3) 2)\n"
	    "   @result{} "1000"
(number->string (ash #b1010 -1) 2)
   @result{} "101"
@end lisp")
#define FUNC_NAME s_scm_ash
{
  /* GJB:FIXME:: what is going on here? */
  SCM res = SCM_INUM (n);
  SCM_VALIDATE_INUM (2,cnt);
#ifdef SCM_BIGDIG
  if (cnt < 0)
    {
      res = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-SCM_INUM (cnt)));
      if (SCM_NFALSEP (scm_negative_p (n)))
	return scm_sum (SCM_MAKINUM (-1L),
			scm_quotient (scm_sum (SCM_MAKINUM (1L), n), res));
      else
	return scm_quotient (n, res);
    }
  else
    return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt));
#else
  SCM_VALIDATE_INUM (1,n)
  cnt = SCM_INUM (cnt);
  if (cnt < 0)
    return SCM_MAKINUM (SCM_SRS (res, -cnt));
  res = SCM_MAKINUM (res << cnt);
  if (SCM_INUM (res) >> cnt != SCM_INUM (n))
    scm_num_overflow (FUNC_NAME);
  return res;
#endif
}
#undef FUNC_NAME

/* GJB:FIXME: do not use SCMs as integers! */
SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0,
            (SCM n, SCM start, SCM end),
	    "Returns the integer composed of the @var{start} (inclusive) through\n"
	    "@var{end} (exclusive) bits of @var{n}.  The @var{start}th bit becomes\n"
	    "the 0-th bit in the result.@refill\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(number->string (bit-extract #b1101101010 0 4) 2)\n"
	    "   @result{} \"1010\"\n"
	    "(number->string (bit-extract #b1101101010 4 9) 2)\n"
	    "   @result{} \"10110\"\n"
	    "@end lisp")
#define FUNC_NAME s_scm_bit_extract
{
  int istart, iend;
  SCM_VALIDATE_INUM (1,n);
  SCM_VALIDATE_INUM_MIN_COPY (2,start,0,istart);
  SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend);
  SCM_ASSERT_RANGE (3, end, (iend >= istart));
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (n))
    return
      scm_logand (scm_difference (scm_integer_expt (SCM_MAKINUM (2),
						    SCM_MAKINUM (iend - istart)),
				  SCM_MAKINUM (1L)),
		  scm_ash (n, SCM_MAKINUM (-istart)));
#else
  SCM_VALIDATE_INUM (1,n);
#endif
  return SCM_MAKINUM ((SCM_INUM (n) >> istart) & ((1L << (iend - istart)) - 1));
}
#undef FUNC_NAME

static const char scm_logtab[] = {
  0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
};

SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0,
            (SCM n),
	    "Returns the number of bits in integer @var{n}.  If integer is positive,\n"
	    "the 1-bits in its binary representation are counted.  If negative, the\n"
	    "0-bits in its two's-complement binary representation are counted.  If 0,\n"
	    "0 is returned.\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(logcount #b10101010)\n"
	    "   @result{} 4\n"
	    "(logcount 0)\n"
	    "   @result{} 0\n"
	    "(logcount -2)\n"
	    "   @result{} 1\n"
	    "@end lisp")
#define FUNC_NAME s_scm_logcount
{
  register unsigned long c = 0;
  register long nn;
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (n))
    {
      scm_sizet i;
      SCM_BIGDIG *ds, d;
      SCM_VALIDATE_BIGINT (1,n);
      if (SCM_BIGSIGN (n))
	return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n));
      ds = SCM_BDIGITS (n);
      for (i = SCM_NUMDIGS (n); i--;)
	for (d = ds[i]; d; d >>= 4)
	  c += scm_logtab[15 & d];
      return SCM_MAKINUM (c);
    }
#else
  SCM_VALIDATE_INUM (1,n);
#endif
  if ((nn = SCM_INUM (n)) < 0)
    nn = -1 - nn;
  for (; nn; nn >>= 4)
    c += scm_logtab[15 & nn];
  return SCM_MAKINUM (c);
}
#undef FUNC_NAME


static const char scm_ilentab[] = {
  0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4
};

SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0,
            (SCM n),
	    "Returns the number of bits neccessary to represent @var{n}.\n\n"
	    "Example:\n"
	    "@lisp\n"
	    "(integer-length #b10101010)\n"
	    "   @result{} 8\n"
	    "(integer-length 0)\n"
	    "   @result{} 0\n"
	    "(integer-length #b1111)\n"
	    "   @result{} 4\n"
	    "@end lisp")
#define FUNC_NAME s_scm_integer_length
{
  register unsigned long c = 0;
  register long nn;
  unsigned int l = 4;
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (n))
    {
      SCM_BIGDIG *ds, d;
      SCM_VALIDATE_BIGINT (1,n);
      if (SCM_BIGSIGN (n))
	return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n));
      ds = SCM_BDIGITS (n);
      d = ds[c = SCM_NUMDIGS (n) - 1];
      for (c *= SCM_BITSPERDIG; d; d >>= 4)
	{
	  c += 4;
	  l = scm_ilentab[15 & d];
	}
      return SCM_MAKINUM (c - 4 + l);
    }
#else
  SCM_VALIDATE_INUM (1,n);
#endif
  if ((nn = SCM_INUM (n)) < 0)
    nn = -1 - nn;
  for (; nn; nn >>= 4)
    {
      c += 4;
      l = scm_ilentab[15 & nn];
    }
  return SCM_MAKINUM (c - 4 + l);
}
#undef FUNC_NAME


#ifdef SCM_BIGDIG
static const char s_bignum[] = "bignum";

SCM
scm_mkbig (scm_sizet nlen, int sign)
{
  SCM v = nlen;
  /* Cast to SCM to avoid signed/unsigned comparison warnings.  */
  if (((v << 16) >> 16) != (SCM) nlen)
    scm_wta (SCM_MAKINUM (nlen), (char *) SCM_NALLOC, s_bignum);
  SCM_NEWCELL (v);
  SCM_DEFER_INTS;
  SCM_SETCHARS (v, scm_must_malloc ((long) (nlen * sizeof (SCM_BIGDIG)),
				    s_bignum));
  SCM_SETNUMDIGS (v, nlen, sign ? scm_tc16_bigneg : scm_tc16_bigpos);
  SCM_ALLOW_INTS;
  return v;
}


SCM
scm_big2inum (SCM b, scm_sizet l)
{
  unsigned long num = 0;
  SCM_BIGDIG *tmp = SCM_BDIGITS (b);
  while (l--)
    num = SCM_BIGUP (num) + tmp[l];
  if (SCM_TYP16 (b) == scm_tc16_bigpos)
    {
      if (SCM_POSFIXABLE (num))
	return SCM_MAKINUM (num);
    }
  else if (SCM_UNEGFIXABLE (num))
    return SCM_MAKINUM (-num);
  return b;
}


static const char s_adjbig[] = "scm_adjbig";

SCM
scm_adjbig (SCM b, scm_sizet nlen)
{
  scm_sizet nsiz = nlen;
  if (((nsiz << 16) >> 16) != nlen)
    scm_wta (scm_ulong2num (nsiz), (char *) SCM_NALLOC, s_adjbig);

  SCM_DEFER_INTS;
  {
    SCM_BIGDIG *digits
      = ((SCM_BIGDIG *)
	 scm_must_realloc ((char *) SCM_CHARS (b),
			   (long) (SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG)),
			   (long) (nsiz * sizeof (SCM_BIGDIG)), s_adjbig));

    SCM_SETCHARS (b, digits);
    SCM_SETNUMDIGS (b, nsiz, SCM_TYP16 (b));
  }
  SCM_ALLOW_INTS;
  return b;
}


SCM
scm_normbig (SCM b)
{
#ifndef _UNICOS
  scm_sizet nlen = SCM_NUMDIGS (b);
#else
  int nlen = SCM_NUMDIGS (b); /* unsigned nlen breaks on Cray when nlen => 0 */
#endif
  SCM_BIGDIG *zds = SCM_BDIGITS (b);
  while (nlen-- && !zds[nlen]);
  nlen++;
  if (nlen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM))
    if (SCM_INUMP (b = scm_big2inum (b, (scm_sizet) nlen)))
      return b;
  if (SCM_NUMDIGS (b) == nlen)
    return b;
  return scm_adjbig (b, (scm_sizet) nlen);
}


SCM
scm_copybig (SCM b, int sign)
{
  scm_sizet i = SCM_NUMDIGS (b);
  SCM ans = scm_mkbig (i, sign);
  SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans);
  while (i--)
    dst[i] = src[i];
  return ans;
}


SCM
scm_long2big (long n)
{
  scm_sizet i = 0;
  SCM_BIGDIG *digits;
  SCM ans = scm_mkbig (SCM_DIGSPERLONG, n < 0);
  digits = SCM_BDIGITS (ans);
  if (n < 0)
    n = -n;
  while (i < SCM_DIGSPERLONG)
    {
      digits[i++] = SCM_BIGLO (n);
      n = SCM_BIGDN ((unsigned long) n);
    }
  return ans;
}

#ifdef HAVE_LONG_LONGS

SCM
scm_long_long2big (long_long n)
{
  scm_sizet i;
  SCM_BIGDIG *digits;
  SCM ans;
  int n_digits;

  {
    long tn;
    tn = (long) n;
    if ((long long) tn == n)
      return scm_long2big (tn);
  }

  {
    long_long tn;

    for (tn = n, n_digits = 0;
	 tn;
	 ++n_digits, tn = SCM_BIGDN ((ulong_long) tn))
      ;
  }

  i = 0;
  ans = scm_mkbig (n_digits, n < 0);
  digits = SCM_BDIGITS (ans);
  if (n < 0)
    n = -n;
  while (i < n_digits)
    {
      digits[i++] = SCM_BIGLO (n);
      n = SCM_BIGDN ((ulong_long) n);
    }
  return ans;
}
#endif


SCM
scm_2ulong2big (unsigned long *np)
{
  unsigned long n;
  scm_sizet i;
  SCM_BIGDIG *digits;
  SCM ans;

  ans = scm_mkbig (2 * SCM_DIGSPERLONG, 0);
  digits = SCM_BDIGITS (ans);

  n = np[0];
  for (i = 0; i < SCM_DIGSPERLONG; ++i)
    {
      digits[i] = SCM_BIGLO (n);
      n = SCM_BIGDN ((unsigned long) n);
    }
  n = np[1];
  for (i = 0; i < SCM_DIGSPERLONG; ++i)
    {
      digits[i + SCM_DIGSPERLONG] = SCM_BIGLO (n);
      n = SCM_BIGDN ((unsigned long) n);
    }
  return ans;
}


SCM
scm_ulong2big (unsigned long n)
{
  scm_sizet i = 0;
  SCM_BIGDIG *digits;
  SCM ans = scm_mkbig (SCM_DIGSPERLONG, 0);
  digits = SCM_BDIGITS (ans);
  while (i < SCM_DIGSPERLONG)
    {
      digits[i++] = SCM_BIGLO (n);
      n = SCM_BIGDN (n);
    }
  return ans;
}


int
scm_bigcomp (SCM x, SCM y)
{
  int xsign = SCM_BIGSIGN (x);
  int ysign = SCM_BIGSIGN (y);
  scm_sizet xlen, ylen;

  /* Look at the signs, first.  */
  if (ysign < xsign)
    return 1;
  if (ysign > xsign)
    return -1;

  /* They're the same sign, so see which one has more digits.  Note
     that, if they are negative, the longer number is the lesser.  */
  ylen = SCM_NUMDIGS (y);
  xlen = SCM_NUMDIGS (x);
  if (ylen > xlen)
    return (xsign) ? -1 : 1;
  if (ylen < xlen)
    return (xsign) ? 1 : -1;

  /* They have the same number of digits, so find the most significant
     digit where they differ.  */
  while (xlen)
    {
      --xlen;
      if (SCM_BDIGITS (y)[xlen] != SCM_BDIGITS (x)[xlen])
	/* Make the discrimination based on the digit that differs.  */
	return ((SCM_BDIGITS (y)[xlen] > SCM_BDIGITS (x)[xlen])
		? (xsign ? -1 :  1)
		: (xsign ?  1 : -1));
    }

  /* The numbers are identical.  */
  return 0;
}

#ifndef SCM_DIGSTOOBIG


long
scm_pseudolong (long x)
{
  union
  {
    long l;
    SCM_BIGDIG bd[SCM_DIGSPERLONG];
  }
  p;
  scm_sizet i = 0;
  if (x < 0)
    x = -x;
  while (i < SCM_DIGSPERLONG)
    {
      p.bd[i++] = SCM_BIGLO (x);
      x = SCM_BIGDN (x);
    }
  /*  p.bd[0] = SCM_BIGLO(x); p.bd[1] = SCM_BIGDN(x); */
  return p.l;
}

#else


void
scm_longdigs (long x, SCM_BIGDIG digs[])
{
  scm_sizet i = 0;
  if (x < 0)
    x = -x;
  while (i < SCM_DIGSPERLONG)
    {
      digs[i++] = SCM_BIGLO (x);
      x = SCM_BIGDN (x);
    }
}
#endif


SCM
scm_addbig (SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int sgny)
{
  /* Assumes nx <= SCM_NUMDIGS(bigy) */
  /* Assumes xsgn and sgny scm_equal either 0 or 0x0100 */
  long num = 0;
  scm_sizet i = 0, ny = SCM_NUMDIGS (bigy);
  SCM z = scm_copybig (bigy, SCM_BIGSIGN (bigy) ^ sgny);
  SCM_BIGDIG *zds = SCM_BDIGITS (z);
  if (xsgn ^ SCM_BIGSIGN (z))
    {
      do
	{
	  num += (long) zds[i] - x[i];
	  if (num < 0)
	    {
	      zds[i] = num + SCM_BIGRAD;
	      num = -1;
	    }
	  else
	    {
	      zds[i] = SCM_BIGLO (num);
	      num = 0;
	    }
	}
      while (++i < nx);
      if (num && nx == ny)
	{
	  num = 1;
	  i = 0;
	  SCM_SETCAR (z, SCM_CAR (z) ^ 0x0100);
	  do
	    {
	      num += (SCM_BIGRAD - 1) - zds[i];
	      zds[i++] = SCM_BIGLO (num);
	      num = SCM_BIGDN (num);
	    }
	  while (i < ny);
	}
      else
	while (i < ny)
	  {
	    num += zds[i];
	    if (num < 0)
	      {
		zds[i++] = num + SCM_BIGRAD;
		num = -1;
	      }
	    else
	      {
		zds[i++] = SCM_BIGLO (num);
		num = 0;
	      }
	  }
    }
  else
    {
      do
	{
	  num += (long) zds[i] + x[i];
	  zds[i++] = SCM_BIGLO (num);
	  num = SCM_BIGDN (num);
	}
      while (i < nx);
      if (!num)
	return z;
      while (i < ny)
	{
	  num += zds[i];
	  zds[i++] = SCM_BIGLO (num);
	  num = SCM_BIGDN (num);
	  if (!num)
	    return z;
	}
      if (num)
	{
	  z = scm_adjbig (z, ny + 1);
	  SCM_BDIGITS (z)[ny] = num;
	  return z;
	}
    }
  return scm_normbig (z);
}


SCM
scm_mulbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn)
{
  scm_sizet i = 0, j = nx + ny;
  unsigned long n = 0;
  SCM z = scm_mkbig (j, sgn);
  SCM_BIGDIG *zds = SCM_BDIGITS (z);
  while (j--)
    zds[j] = 0;
  do
    {
      j = 0;
      if (x[i])
	{
	  do
	    {
	      n += zds[i + j] + ((unsigned long) x[i] * y[j]);
	      zds[i + j++] = SCM_BIGLO (n);
	      n = SCM_BIGDN (n);
	    }
	  while (j < ny);
	  if (n)
	    {
	      zds[i + j] = n;
	      n = 0;
	    }
	}
    }
  while (++i < nx);
  return scm_normbig (z);
}


/* Sun's compiler complains about the fact that this function has an
   ANSI prototype in numbers.h, but a K&R declaration here, and the
   two specify different promotions for the third argument.  I'm going
   to turn this into an ANSI declaration, and see if anyone complains
   about it not being K&R.  */

unsigned int
scm_divbigdig (SCM_BIGDIG * ds,
	       scm_sizet h,
	       SCM_BIGDIG div)
{
  register unsigned long t2 = 0;
  while (h--)
    {
      t2 = SCM_BIGUP (t2) + ds[h];
      ds[h] = t2 / div;
      t2 %= div;
    }
  return t2;
}


SCM
scm_divbigint (SCM x, long z, int sgn, int mode)
{
  if (z < 0)
    z = -z;
  if (z < SCM_BIGRAD)
    {
      register unsigned long t2 = 0;
      register SCM_BIGDIG *ds = SCM_BDIGITS (x);
      scm_sizet nd = SCM_NUMDIGS (x);
      while (nd--)
	t2 = (SCM_BIGUP (t2) + ds[nd]) % z;
      if (mode && t2)
	t2 = z - t2;
      return SCM_MAKINUM (sgn ? -t2 : t2);
    }
  {
#ifndef SCM_DIGSTOOBIG
    unsigned long t2 = scm_pseudolong (z);
    return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			  (SCM_BIGDIG *) & t2, SCM_DIGSPERLONG,
			  sgn, mode);
#else
    SCM_BIGDIG t2[SCM_DIGSPERLONG];
    scm_longdigs (z, t2);
    return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			  t2, SCM_DIGSPERLONG,
			  sgn, mode);
#endif
  }
}


SCM
scm_divbigbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn, int modes)
{
  /* modes description
     0  remainder
     1  scm_modulo
     2  quotient
     3  quotient but returns 0 if division is not exact. */
  scm_sizet i = 0, j = 0;
  long num = 0;
  unsigned long t2 = 0;
  SCM z, newy;
  SCM_BIGDIG d = 0, qhat, *zds, *yds;
  /* algorithm requires nx >= ny */
  if (nx < ny)
    switch (modes)
      {
      case 0:			/* remainder -- just return x */
	z = scm_mkbig (nx, sgn);
	zds = SCM_BDIGITS (z);
	do
	  {
	    zds[i] = x[i];
	  }
	while (++i < nx);
	return z;
      case 1:			/* scm_modulo -- return y-x */
	z = scm_mkbig (ny, sgn);
	zds = SCM_BDIGITS (z);
	do
	  {
	    num += (long) y[i] - x[i];
	    if (num < 0)
	      {
		zds[i] = num + SCM_BIGRAD;
		num = -1;
	      }
	    else
	      {
		zds[i] = num;
		num = 0;
	      }
	  }
	while (++i < nx);
	while (i < ny)
	  {
	    num += y[i];
	    if (num < 0)
	      {
		zds[i++] = num + SCM_BIGRAD;
		num = -1;
	      }
	    else
	      {
		zds[i++] = num;
		num = 0;
	      }
	  }
	goto doadj;
      case 2:
	return SCM_INUM0;	/* quotient is zero */
      case 3:
	return 0;		/* the division is not exact */
      }

  z = scm_mkbig (nx == ny ? nx + 2 : nx + 1, sgn);
  zds = SCM_BDIGITS (z);
  if (nx == ny)
    zds[nx + 1] = 0;
  while (!y[ny - 1])
    ny--;			/* in case y came in as a psuedolong */
  if (y[ny - 1] < (SCM_BIGRAD >> 1))
    {				/* normalize operands */
      d = SCM_BIGRAD / (y[ny - 1] + 1);
      newy = scm_mkbig (ny, 0);
      yds = SCM_BDIGITS (newy);
      while (j < ny)
	{
	  t2 += (unsigned long) y[j] * d;
	  yds[j++] = SCM_BIGLO (t2);
	  t2 = SCM_BIGDN (t2);
	}
      y = yds;
      j = 0;
      t2 = 0;
      while (j < nx)
	{
	  t2 += (unsigned long) x[j] * d;
	  zds[j++] = SCM_BIGLO (t2);
	  t2 = SCM_BIGDN (t2);
	}
      zds[j] = t2;
    }
  else
    {
      zds[j = nx] = 0;
      while (j--)
	zds[j] = x[j];
    }
  j = nx == ny ? nx + 1 : nx;	/* dividend needs more digits than divisor */
  do
    {				/* loop over digits of quotient */
      if (zds[j] == y[ny - 1])
	qhat = SCM_BIGRAD - 1;
      else
	qhat = (SCM_BIGUP (zds[j]) + zds[j - 1]) / y[ny - 1];
      if (!qhat)
	continue;
      i = 0;
      num = 0;
      t2 = 0;
      do
	{			/* multiply and subtract */
	  t2 += (unsigned long) y[i] * qhat;
	  num += zds[j - ny + i] - SCM_BIGLO (t2);
	  if (num < 0)
	    {
	      zds[j - ny + i] = num + SCM_BIGRAD;
	      num = -1;
	    }
	  else
	    {
	      zds[j - ny + i] = num;
	      num = 0;
	    }
	  t2 = SCM_BIGDN (t2);
	}
      while (++i < ny);
      num += zds[j - ny + i] - t2; /* borrow from high digit; don't update */
      while (num)
	{			/* "add back" required */
	  i = 0;
	  num = 0;
	  qhat--;
	  do
	    {
	      num += (long) zds[j - ny + i] + y[i];
	      zds[j - ny + i] = SCM_BIGLO (num);
	      num = SCM_BIGDN (num);
	    }
	  while (++i < ny);
	  num--;
	}
      if (modes & 2)
	zds[j] = qhat;
    }
  while (--j >= ny);
  switch (modes)
    {
    case 3:			/* check that remainder==0 */
      for (j = ny; j && !zds[j - 1]; --j);
      if (j)
	return 0;
    case 2:			/* move quotient down in z */
      j = (nx == ny ? nx + 2 : nx + 1) - ny;
      for (i = 0; i < j; i++)
	zds[i] = zds[i + ny];
      ny = i;
      break;
    case 1:			/* subtract for scm_modulo */
      i = 0;
      num = 0;
      j = 0;
      do
	{
	  num += y[i] - zds[i];
	  j = j | zds[i];
	  if (num < 0)
	    {
	      zds[i] = num + SCM_BIGRAD;
	      num = -1;
	    }
	  else
	    {
	      zds[i] = num;
	      num = 0;
	    }
	}
      while (++i < ny);
      if (!j)
	return SCM_INUM0;
    case 0:			/* just normalize remainder */
      if (d)
	scm_divbigdig (zds, ny, d);
    }
 doadj:
  for (j = ny; j && !zds[j - 1]; --j);
  if (j * SCM_BITSPERDIG <= sizeof (SCM) * SCM_CHAR_BIT)
    if (SCM_INUMP (z = scm_big2inum (z, j)))
      return z;
  return scm_adjbig (z, j);
}
#endif
\f


/*** NUMBERS -> STRINGS ***/
#ifdef SCM_FLOATS
int scm_dblprec;
static const double fx[] =
{  0.0,  5e-1,  5e-2,  5e-3,   5e-4, 5e-5,
  5e-6,  5e-7,  5e-8,  5e-9,  5e-10,
 5e-11, 5e-12, 5e-13, 5e-14,  5e-15,
 5e-16, 5e-17, 5e-18, 5e-19,  5e-20};


static scm_sizet
idbl2str (double f, char *a)
{
  int efmt, dpt, d, i, wp = scm_dblprec;
  scm_sizet ch = 0;
  int exp = 0;

  if (f == 0.0)
    goto zero;			/*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */
  if (f < 0.0)
    {
      f = -f;
      a[ch++] = '-';
    }
  else if (f > 0.0);
  else
    goto funny;
  if (IS_INF (f))
    {
      if (ch == 0)
	a[ch++] = '+';
    funny:
      a[ch++] = '#';
      a[ch++] = '.';
      a[ch++] = '#';
      return ch;
    }
#ifdef DBL_MIN_10_EXP  /* Prevent unnormalized values, as from 
			  make-uniform-vector, from causing infinite loops. */
  while (f < 1.0)
    {
      f *= 10.0;
      if (exp-- < DBL_MIN_10_EXP)
	goto funny;
    }
  while (f > 10.0)
    {
      f *= 0.10;
      if (exp++ > DBL_MAX_10_EXP)
	goto funny;
    }
#else
  while (f < 1.0)
    {
      f *= 10.0;
      exp--;
    }
  while (f > 10.0)
    {
      f /= 10.0;
      exp++;
    }
#endif
  if (f + fx[wp] >= 10.0)
    {
      f = 1.0;
      exp++;
    }
 zero:
#ifdef ENGNOT
  dpt = (exp + 9999) % 3;
  exp -= dpt++;
  efmt = 1;
#else
  efmt = (exp < -3) || (exp > wp + 2);
  if (!efmt)
    {
      if (exp < 0)
	{
	  a[ch++] = '0';
	  a[ch++] = '.';
	  dpt = exp;
	  while (++dpt)
	    a[ch++] = '0';
	}
      else
	dpt = exp + 1;
    }
  else
    dpt = 1;
#endif

  do
    {
      d = f;
      f -= d;
      a[ch++] = d + '0';
      if (f < fx[wp])
	break;
      if (f + fx[wp] >= 1.0)
	{
	  a[ch - 1]++;
	  break;
	}
      f *= 10.0;
      if (!(--dpt))
	a[ch++] = '.';
    }
  while (wp--);

  if (dpt > 0)
    {
#ifndef ENGNOT
      if ((dpt > 4) && (exp > 6))
	{
	  d = (a[0] == '-' ? 2 : 1);
	  for (i = ch++; i > d; i--)
	    a[i] = a[i - 1];
	  a[d] = '.';
	  efmt = 1;
	}
      else
#endif
	{
	  while (--dpt)
	    a[ch++] = '0';
	  a[ch++] = '.';
	}
    }
  if (a[ch - 1] == '.')
    a[ch++] = '0';		/* trailing zero */
  if (efmt && exp)
    {
      a[ch++] = 'e';
      if (exp < 0)
	{
	  exp = -exp;
	  a[ch++] = '-';
	}
      for (i = 10; i <= exp; i *= 10);
      for (i /= 10; i; i /= 10)
	{
	  a[ch++] = exp / i + '0';
	  exp %= i;
	}
    }
  return ch;
}


static scm_sizet
iflo2str (SCM flt, char *str)
{
  scm_sizet i;
#ifdef SCM_SINGLES
  if (SCM_SINGP (flt))
    i = idbl2str (SCM_FLO (flt), str);
  else
#endif
    i = idbl2str (SCM_REAL (flt), str);
  if (SCM_CPLXP (flt))
    {
      if (0 <= SCM_IMAG (flt))	/* jeh */
	str[i++] = '+';		/* jeh */
      i += idbl2str (SCM_IMAG (flt), &str[i]);
      str[i++] = 'i';
    }
  return i;
}
#endif /* SCM_FLOATS */

/* convert a long to a string (unterminated).  returns the number of
   characters in the result. 
   rad is output base
   p is destination: worst case (base 2) is SCM_INTBUFLEN  */
scm_sizet
scm_iint2str (long num, int rad, char *p)
{
  scm_sizet j = 1;
  scm_sizet i;
  unsigned long n = (num < 0) ? -num : num;

  for (n /= rad; n > 0; n /= rad)
    j++;

  i = j;
  if (num < 0)
    {
      *p++ = '-';
      j++;
      n = -num;
    }
  else
    n = num;
  while (i--)
    {
      int d = n % rad;

      n /= rad;
      p[i] = d + ((d < 10) ? '0' : 'a' - 10);
    }
  return j;
}


#ifdef SCM_BIGDIG

static SCM
big2str (SCM b, unsigned int radix)
{
  SCM t = scm_copybig (b, 0);	/* sign of temp doesn't matter */
  register SCM_BIGDIG *ds = SCM_BDIGITS (t);
  scm_sizet i = SCM_NUMDIGS (t);
  scm_sizet j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2
    : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2
    : (SCM_BITSPERDIG * i) + 2;
  scm_sizet k = 0;
  scm_sizet radct = 0;
  scm_sizet ch;			/* jeh */
  SCM_BIGDIG radpow = 1, radmod = 0;
  SCM ss = scm_makstr ((long) j, 0);
  char *s = SCM_CHARS (ss), c;
  while ((long) radpow * radix < SCM_BIGRAD)
    {
      radpow *= radix;
      radct++;
    }
  s[0] = scm_tc16_bigneg == SCM_TYP16 (b) ? '-' : '+';
  while ((i || radmod) && j)
    {
      if (k == 0)
	{
	  radmod = (SCM_BIGDIG) scm_divbigdig (ds, i, radpow);
	  k = radct;
	  if (!ds[i - 1])
	    i--;
	}
      c = radmod % radix;
      radmod /= radix;
      k--;
      s[--j] = c < 10 ? c + '0' : c + 'a' - 10;
    }
  ch = s[0] == '-' ? 1 : 0;	/* jeh */
  if (ch < j)
    {				/* jeh */
      for (i = j; j < SCM_LENGTH (ss); j++)
	s[ch + j - i] = s[j];	/* jeh */
      scm_vector_set_length_x (ss, /* jeh */
			       (SCM) SCM_MAKINUM (ch + SCM_LENGTH (ss) - i));
    }

  return scm_return_first (ss, t);
}
#endif


SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0,
            (SCM x, SCM radix),
	    "")
#define FUNC_NAME s_scm_number_to_string
{
  int base;
  SCM_VALIDATE_INUM_MIN_DEF_COPY (2,radix,2,10,base);
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
      char num_buf[SCM_FLOBUFLEN];
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (x), badx);
      if (SCM_BIGP (x))
	return big2str (x, (unsigned int) base);
#ifndef SCM_RECKLESS
      if (!SCM_INEXP (x))
	{
	badx:
	  SCM_WTA (1, x);
	}
#endif
#else
      SCM_ASSERT (SCM_INEXP (x),
		  x, SCM_ARG1, s_number_to_string);
#endif
      return scm_makfromstr (num_buf, iflo2str (x, num_buf), 0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_ASSERT (SCM_BIGP (x),
		  x, SCM_ARG1, s_number_to_string);
      return big2str (x, (unsigned int) base);
    }
#else
  SCM_ASSERT (SCM_INUMP (x), x, SCM_ARG1, s_number_to_string);
#endif
#endif
  {
    char num_buf[SCM_INTBUFLEN];
    return scm_makfromstr (num_buf,
			   scm_iint2str (SCM_INUM (x),
					 base,
					 num_buf),
			   0);
  }
}
#undef FUNC_NAME


/* These print routines are stubbed here so that scm_repl.c doesn't need
   SCM_FLOATS or SCM_BIGDIGs conditionals */

int
scm_floprint (SCM sexp, SCM port, scm_print_state *pstate)
{
#ifdef SCM_FLOATS
  char num_buf[SCM_FLOBUFLEN];
  scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port);
#else
  scm_ipruk ("float", sexp, port);
#endif
  return !0;
}


int
scm_bigprint (SCM exp, SCM port, scm_print_state *pstate)
{
#ifdef SCM_BIGDIG
  exp = big2str (exp, (unsigned int) 10);
  scm_lfwrite (SCM_CHARS (exp), (scm_sizet) SCM_LENGTH (exp), port);
#else
  scm_ipruk ("bignum", exp, port);
#endif
  return !0;
}
/*** END nums->strs ***/

/*** STRINGS -> NUMBERS ***/

static SCM
scm_small_istr2int (char *str, long len, long radix)
{
  register long n = 0, ln;
  register int c;
  register int i = 0;
  int lead_neg = 0;
  if (0 >= len)
    return SCM_BOOL_F;		/* zero scm_length */
  switch (*str)
    {				/* leading sign */
    case '-':
      lead_neg = 1;
    case '+':
      if (++i == len)
	return SCM_BOOL_F;	/* bad if lone `+' or `-' */
    }

  do
    {
      switch (c = str[i++])
	{
	case DIGITS:
	  c = c - '0';
	  goto accumulate;
	case 'A':
	case 'B':
	case 'C':
	case 'D':
	case 'E':
	case 'F':
	  c = c - 'A' + 10;
	  goto accumulate;
	case 'a':
	case 'b':
	case 'c':
	case 'd':
	case 'e':
	case 'f':
	  c = c - 'a' + 10;
	accumulate:
	  if (c >= radix)
	    return SCM_BOOL_F;	/* bad digit for radix */
	  ln = n;
	  n = n * radix - c;
	  /* Negation is a workaround for HP700 cc bug */
	  if (n > ln || (-n > -SCM_MOST_NEGATIVE_FIXNUM))
	    goto ovfl;
	  break;
	default:
	  return SCM_BOOL_F;	/* not a digit */
	}
    }
  while (i < len);
  if (!lead_neg)
    if ((n = -n) > SCM_MOST_POSITIVE_FIXNUM)
      goto ovfl;
  return SCM_MAKINUM (n);
 ovfl:				/* overflow scheme integer */
  return SCM_BOOL_F;
}


SCM
scm_istr2int (char *str, long len, long radix)
{
  scm_sizet j;
  register scm_sizet k, blen = 1;
  scm_sizet i = 0;
  int c;
  SCM res;
  register SCM_BIGDIG *ds;
  register unsigned long t2;

  if (0 >= len)
    return SCM_BOOL_F;		/* zero scm_length */

  /* Short numbers we parse directly into an int, to avoid the overhead 
     of creating a bignum.  */
  if (len < 6)
    return scm_small_istr2int (str, len, radix);

  if (16 == radix)
    j = 1 + (4 * len * sizeof (char)) / (SCM_BITSPERDIG);
  else if (10 <= radix)
    j = 1 + (84 * len * sizeof (char)) / (SCM_BITSPERDIG * 25);
  else
    j = 1 + (len * sizeof (char)) / (SCM_BITSPERDIG);
  switch (str[0])
    {				/* leading sign */
    case '-':
    case '+':
      if (++i == (unsigned) len)
	return SCM_BOOL_F;	/* bad if lone `+' or `-' */
    }
  res = scm_mkbig (j, '-' == str[0]);
  ds = SCM_BDIGITS (res);
  for (k = j; k--;)
    ds[k] = 0;
  do
    {
      switch (c = str[i++])
	{
	case DIGITS:
	  c = c - '0';
	  goto accumulate;
	case 'A':
	case 'B':
	case 'C':
	case 'D':
	case 'E':
	case 'F':
	  c = c - 'A' + 10;
	  goto accumulate;
	case 'a':
	case 'b':
	case 'c':
	case 'd':
	case 'e':
	case 'f':
	  c = c - 'a' + 10;
	accumulate:
	  if (c >= radix)
	    return SCM_BOOL_F;	/* bad digit for radix */
	  k = 0;
	  t2 = c;
	moretodo:
	  while (k < blen)
	    {
/* printf ("k = %d, blen = %d, t2 = %ld, ds[k] = %d\n", k, blen, t2, ds[k]); */
	      t2 += ds[k] * radix;
	      ds[k++] = SCM_BIGLO (t2);
	      t2 = SCM_BIGDN (t2);
	    }
	  if (blen > j)
	    scm_num_overflow ("bignum");
	  if (t2)
	    {
	      blen++;
	      goto moretodo;
	    }
	  break;
	default:
	  return SCM_BOOL_F;	/* not a digit */
	}
    }
  while (i < (unsigned) len);
  if (blen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM))
    if (SCM_INUMP (res = scm_big2inum (res, blen)))
      return res;
  if (j == blen)
    return res;
  return scm_adjbig (res, blen);
}

#ifdef SCM_FLOATS

SCM
scm_istr2flo (char *str, long len, long radix)
{
  register int c, i = 0;
  double lead_sgn;
  double res = 0.0, tmp = 0.0;
  int flg = 0;
  int point = 0;
  SCM second;

  if (i >= len)
    return SCM_BOOL_F;		/* zero scm_length */

  switch (*str)
    {				/* leading sign */
    case '-':
      lead_sgn = -1.0;
      i++;
      break;
    case '+':
      lead_sgn = 1.0;
      i++;
      break;
    default:
      lead_sgn = 0.0;
    }
  if (i == len)
    return SCM_BOOL_F;		/* bad if lone `+' or `-' */

  if (str[i] == 'i' || str[i] == 'I')
    {				/* handle `+i' and `-i'   */
      if (lead_sgn == 0.0)
	return SCM_BOOL_F;	/* must have leading sign */
      if (++i < len)
	return SCM_BOOL_F;	/* `i' not last character */
      return scm_makdbl (0.0, lead_sgn);
    }
  do
    {				/* check initial digits */
      switch (c = str[i])
	{
	case DIGITS:
	  c = c - '0';
	  goto accum1;
	case 'D':
	case 'E':
	case 'F':
	  if (radix == 10)
	    goto out1;		/* must be exponent */
	case 'A':
	case 'B':
	case 'C':
	  c = c - 'A' + 10;
	  goto accum1;
	case 'd':
	case 'e':
	case 'f':
	  if (radix == 10)
	    goto out1;
	case 'a':
	case 'b':
	case 'c':
	  c = c - 'a' + 10;
	accum1:
	  if (c >= radix)
	    return SCM_BOOL_F;	/* bad digit for radix */
	  res = res * radix + c;
	  flg = 1;		/* res is valid */
	  break;
	default:
	  goto out1;
	}
    }
  while (++i < len);
 out1:

  /* if true, then we did see a digit above, and res is valid */
  if (i == len)
    goto done;

  /* By here, must have seen a digit,
     or must have next char be a `.' with radix==10 */
  if (!flg)
    if (!(str[i] == '.' && radix == 10))
      return SCM_BOOL_F;

  while (str[i] == '#')
    {				/* optional sharps */
      res *= radix;
      if (++i == len)
	goto done;
    }

  if (str[i] == '/')
    {
      while (++i < len)
	{
	  switch (c = str[i])
	    {
	    case DIGITS:
	      c = c - '0';
	      goto accum2;
	    case 'A':
	    case 'B':
	    case 'C':
	    case 'D':
	    case 'E':
	    case 'F':
	      c = c - 'A' + 10;
	      goto accum2;
	    case 'a':
	    case 'b':
	    case 'c':
	    case 'd':
	    case 'e':
	    case 'f':
	      c = c - 'a' + 10;
	    accum2:
	      if (c >= radix)
		return SCM_BOOL_F;
	      tmp = tmp * radix + c;
	      break;
	    default:
	      goto out2;
	    }
	}
    out2:
      if (tmp == 0.0)
	return SCM_BOOL_F;	/* `slash zero' not allowed */
      if (i < len)
	while (str[i] == '#')
	  {			/* optional sharps */
	    tmp *= radix;
	    if (++i == len)
	      break;
	  }
      res /= tmp;
      goto done;
    }

  if (str[i] == '.')
    {				/* decimal point notation */
      if (radix != 10)
	return SCM_BOOL_F;	/* must be radix 10 */
      while (++i < len)
	{
	  switch (c = str[i])
	    {
	    case DIGITS:
	      point--;
	      res = res * 10.0 + c - '0';
	      flg = 1;
	      break;
	    default:
	      goto out3;
	    }
	}
    out3:
      if (!flg)
	return SCM_BOOL_F;	/* no digits before or after decimal point */
      if (i == len)
	goto adjust;
      while (str[i] == '#')
	{			/* ignore remaining sharps */
	  if (++i == len)
	    goto adjust;
	}
    }

  switch (str[i])
    {				/* exponent */
    case 'd':
    case 'D':
    case 'e':
    case 'E':
    case 'f':
    case 'F':
    case 'l':
    case 'L':
    case 's':
    case 'S':
      {
	int expsgn = 1, expon = 0;
	if (radix != 10)
	  return SCM_BOOL_F;	/* only in radix 10 */
	if (++i == len)
	  return SCM_BOOL_F;	/* bad exponent */
	switch (str[i])
	  {
	  case '-':
	    expsgn = (-1);
	  case '+':
	    if (++i == len)
	      return SCM_BOOL_F;	/* bad exponent */
	  }
	if (str[i] < '0' || str[i] > '9')
	  return SCM_BOOL_F;	/* bad exponent */
	do
	  {
	    switch (c = str[i])
	      {
	      case DIGITS:
		expon = expon * 10 + c - '0';
		if (expon > MAXEXP)
		  return SCM_BOOL_F;	/* exponent too large */
		break;
	      default:
		goto out4;
	      }
	  }
	while (++i < len);
      out4:
	point += expsgn * expon;
      }
    }

 adjust:
  if (point >= 0)
    while (point--)
      res *= 10.0;
  else
#ifdef _UNICOS
    while (point++)
      res *= 0.1;
#else
  while (point++)
    res /= 10.0;
#endif

 done:
  /* at this point, we have a legitimate floating point result */
  if (lead_sgn == -1.0)
    res = -res;
  if (i == len)
    return scm_makdbl (res, 0.0);

  if (str[i] == 'i' || str[i] == 'I')
    {				/* pure imaginary number  */
      if (lead_sgn == 0.0)
	return SCM_BOOL_F;	/* must have leading sign */
      if (++i < len)
	return SCM_BOOL_F;	/* `i' not last character */
      return scm_makdbl (0.0, res);
    }

  switch (str[i++])
    {
    case '-':
      lead_sgn = -1.0;
      break;
    case '+':
      lead_sgn = 1.0;
      break;
    case '@':
      {				/* polar input for complex number */
	/* get a `real' for scm_angle */
	second = scm_istr2flo (&str[i], (long) (len - i), radix);
	if (!SCM_INEXP (second))
	  return SCM_BOOL_F;	/* not `real' */
	if (SCM_CPLXP (second))
	  return SCM_BOOL_F;	/* not `real' */
	tmp = SCM_REALPART (second);
	return scm_makdbl (res * cos (tmp), res * sin (tmp));
      }
    default:
      return SCM_BOOL_F;
    }

  /* at this point, last char must be `i' */
  if (str[len - 1] != 'i' && str[len - 1] != 'I')
    return SCM_BOOL_F;
  /* handles `x+i' and `x-i' */
  if (i == (len - 1))
    return scm_makdbl (res, lead_sgn);
  /* get a `ureal' for complex part */
  second = scm_istr2flo (&str[i], (long) ((len - i) - 1), radix);
  if (!SCM_INEXP (second))
    return SCM_BOOL_F;		/* not `ureal' */
  if (SCM_CPLXP (second))
    return SCM_BOOL_F;		/* not `ureal' */
  tmp = SCM_REALPART (second);
  if (tmp < 0.0)
    return SCM_BOOL_F;		/* not `ureal' */
  return scm_makdbl (res, (lead_sgn * tmp));
}
#endif /* SCM_FLOATS */


SCM
scm_istring2number (char *str, long len, long radix)
{
  int i = 0;
  char ex = 0;
  char ex_p = 0, rx_p = 0;	/* Only allow 1 exactness and 1 radix prefix */
  SCM res;
  if (len == 1)
    if (*str == '+' || *str == '-')    /* Catches lone `+' and `-' for speed */
      return SCM_BOOL_F;

  while ((len - i) >= 2 && str[i] == '#' && ++i)
    switch (str[i++])
      {
      case 'b':
      case 'B':
	if (rx_p++)
	  return SCM_BOOL_F;
	radix = 2;
	break;
      case 'o':
      case 'O':
	if (rx_p++)
	  return SCM_BOOL_F;
	radix = 8;
	break;
      case 'd':
      case 'D':
	if (rx_p++)
	  return SCM_BOOL_F;
	radix = 10;
	break;
      case 'x':
      case 'X':
	if (rx_p++)
	  return SCM_BOOL_F;
	radix = 16;
	break;
      case 'i':
      case 'I':
	if (ex_p++)
	  return SCM_BOOL_F;
	ex = 2;
	break;
      case 'e':
      case 'E':
	if (ex_p++)
	  return SCM_BOOL_F;
	ex = 1;
	break;
      default:
	return SCM_BOOL_F;
      }

  switch (ex)
    {
    case 1:
      return scm_istr2int (&str[i], len - i, radix);
    case 0:
      res = scm_istr2int (&str[i], len - i, radix);
      if (SCM_NFALSEP (res))
	return res;
#ifdef SCM_FLOATS
    case 2:
      return scm_istr2flo (&str[i], len - i, radix);
#endif
    }
  return SCM_BOOL_F;
}


SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0,
            (SCM str, SCM radix),
	    "")
#define FUNC_NAME s_scm_string_to_number
{
  SCM answer;
  int base;
  SCM_VALIDATE_ROSTRING (1,str);
  SCM_VALIDATE_INUM_MIN_DEF_COPY (2,radix,2,10,base);
  answer = scm_istring2number (SCM_ROCHARS (str),
			       SCM_ROLENGTH (str),
                               base);
  return scm_return_first (answer, str);
}
#undef FUNC_NAME
/*** END strs->nums ***/

#ifdef SCM_FLOATS

SCM
scm_makdbl (double x, double y)
{
  SCM z;
  if ((y == 0.0) && (x == 0.0))
    return scm_flo0;
  SCM_DEFER_INTS;
  if (y == 0.0)
    {
#ifdef SCM_SINGLES
      float fx = x;
#ifndef SCM_SINGLESONLY
      if ((-FLTMAX < x) && (x < FLTMAX) && (fx == x))
#endif
	{
          SCM_NEWSMOB(z,scm_tc_flo,NULL);
	  SCM_FLO (z) = x;
	  SCM_ALLOW_INTS;
	  return z;
	}
#endif /* def SCM_SINGLES */
      SCM_NEWSMOB(z,scm_tc_dblr,scm_must_malloc (1L * sizeof (double), "real"));
    }
  else
    {
      SCM_NEWSMOB(z,scm_tc_dblc,scm_must_malloc (2L * sizeof (double), "comkplex"));
      SCM_IMAG (z) = y;
    }
  SCM_REAL (z) = x;
  SCM_ALLOW_INTS;
  return z;
}
#endif


SCM
scm_bigequal (SCM x, SCM y)
{
#ifdef SCM_BIGDIG
  if (0 == scm_bigcomp (x, y))
    return SCM_BOOL_T;
#endif
  return SCM_BOOL_F;
}


SCM
scm_floequal (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  if (SCM_REALPART (x) != SCM_REALPART (y))
    return SCM_BOOL_F;
  if (!(SCM_CPLXP (x) && (SCM_IMAG (x) != SCM_IMAG (y))))
    return SCM_BOOL_T;
#endif
  return SCM_BOOL_F;
}


SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p);

SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, 
            (SCM x),
	    "")
#define FUNC_NAME s_scm_number_p
{
  if (SCM_INUMP (x))
    return SCM_BOOL_T;
#ifdef SCM_FLOATS
  if (SCM_NUMP (x))
    return SCM_BOOL_T;
#else
#ifdef SCM_BIGDIG
  if (SCM_NUMP (x))
    return SCM_BOOL_T;
#endif
#endif
  return SCM_BOOL_F;
}
#undef FUNC_NAME


#ifdef SCM_FLOATS
SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p);


SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0, 
            (SCM x),
	    "")
#define FUNC_NAME s_scm_real_p
{
  if (SCM_INUMP (x))
    return SCM_BOOL_T;
  if (SCM_IMP (x))
    return SCM_BOOL_F;
  if (SCM_REALP (x))
    return SCM_BOOL_T;
#ifdef SCM_BIGDIG
  if (SCM_BIGP (x))
    return SCM_BOOL_T;
#endif
  return SCM_BOOL_F;
}
#undef FUNC_NAME


SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, 
            (SCM x),
	    "")
#define FUNC_NAME s_scm_integer_p
{
  double r;
  if (SCM_INUMP (x))
    return SCM_BOOL_T;
  if (SCM_IMP (x))
    return SCM_BOOL_F;
#ifdef SCM_BIGDIG
  if (SCM_BIGP (x))
    return SCM_BOOL_T;
#endif
  if (!SCM_INEXP (x))
    return SCM_BOOL_F;
  if (SCM_CPLXP (x))
    return SCM_BOOL_F;
  r = SCM_REALPART (x);
  if (r == floor (r))
    return SCM_BOOL_T;
  return SCM_BOOL_F;
}
#undef FUNC_NAME


#endif /* SCM_FLOATS */

SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, 
            (SCM x),
	    "")
#define FUNC_NAME s_scm_inexact_p
{
#ifdef SCM_FLOATS
  if (SCM_INEXP (x))
    return SCM_BOOL_T;
#endif
  return SCM_BOOL_F;
}
#undef FUNC_NAME


SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p);

SCM
scm_num_eq_p (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  SCM t;
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx:
	  SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    return SCM_BOOL_F;
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    return SCM_BOOL(0 == scm_bigcomp (x, y));
	  SCM_ASRTGO (SCM_INEXP (y), bady);
	bigreal:
	  return ((SCM_REALP (y) && (scm_big2dbl (x) == SCM_REALPART (y)))
		  ? SCM_BOOL_T
		  : SCM_BOOL_F);
	}
      SCM_ASRTGO (SCM_INEXP (x), badx);
#else
      SCM_GASSERT2 (SCM_INEXP (x),
		    g_eq_p, x, y, SCM_ARG1, s_eq_p);
#endif
      if (SCM_INUMP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto realint;
	}
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto bigreal;
	}
      SCM_ASRTGO (SCM_INEXP (y), bady);
#else
      SCM_ASRTGO (SCM_INEXP (y), bady);
#endif
      if (SCM_REALPART (x) != SCM_REALPART (y))
	return SCM_BOOL_F;
      if (SCM_CPLXP (x))
	return ((SCM_CPLXP (y) && (SCM_IMAG (x) == SCM_IMAG (y)))
		? SCM_BOOL_T
		: SCM_BOOL_F);
      return SCM_NEGATE_BOOL(SCM_CPLXP (y));
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return SCM_BOOL_F;
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
	}
#else
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
	}
#endif
    realint:
      return ((SCM_REALP (y) && (((double) SCM_INUM (x)) == SCM_REALPART (y)))
	      ? SCM_BOOL_T
	      : SCM_BOOL_F);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_eq_p, x, y, SCM_ARG1, s_eq_p);
      if (SCM_INUMP (y))
	return SCM_BOOL_F;
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return SCM_BOOL(0 == scm_bigcomp (x, y));
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
	}
      return SCM_BOOL_F;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_eq_p, x, y, SCM_ARG1, s_eq_p);
  SCM_GASSERT2 (SCM_INUMP (y), g_eq_p, x, y, SCM_ARGn, s_eq_p);
#endif
#endif
  return SCM_BOOL((long) x == (long) y);
}


SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p);

SCM
scm_less_p (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx:
	  SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    return SCM_BOOL(SCM_BIGSIGN (x));
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    return SCM_BOOL(1 == scm_bigcomp (x, y));
	  SCM_ASRTGO (SCM_REALP (y), bady);
	  return ((scm_big2dbl (x) < SCM_REALPART (y))
		  ? SCM_BOOL_T
		  : SCM_BOOL_F);
	}
      SCM_ASRTGO (SCM_REALP (x), badx);
#else
      SCM_GASSERT2 (SCM_REALP (x),
		    g_less_p, x, y, SCM_ARG1, s_less_p);
#endif
      if (SCM_INUMP (y))
	return ((SCM_REALPART (x) < ((double) SCM_INUM (y)))
		? SCM_BOOL_T
		: SCM_BOOL_F);
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return SCM_BOOL(SCM_REALPART (x) < scm_big2dbl (y));
      SCM_ASRTGO (SCM_REALP (y), bady);
#else
      SCM_ASRTGO (SCM_REALP (y), bady);
#endif
      return SCM_BOOL(SCM_REALPART (x) < SCM_REALPART (y));
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return SCM_NEGATE_BOOL(SCM_BIGSIGN (y));
      if (!SCM_REALP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
	}
#else
      if (!SCM_REALP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
	}
#endif
      return ((((double) SCM_INUM (x)) < SCM_REALPART (y))
	      ? SCM_BOOL_T
	      : SCM_BOOL_F);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_less_p, x, y, SCM_ARG1, s_less_p);
      if (SCM_INUMP (y))
	return SCM_BOOL(SCM_BIGSIGN (x));
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return SCM_BOOL(1 == scm_bigcomp (x, y));
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
	}
      return SCM_NEGATE_BOOL(SCM_BIGSIGN (y));
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_less_p, x, y, SCM_ARG1, s_less_p);
  SCM_GASSERT2 (SCM_INUMP (y), g_less_p, x, y, SCM_ARGn, s_less_p);
#endif
#endif
  return SCM_BOOL((long) x < (long) y);
}


SCM_DEFINE1 (scm_gr_p, ">", scm_tc7_rpsubr,
             (SCM x, SCM y),
	     "")
#define FUNC_NAME s_scm_gr_p
{
  return scm_less_p (y, x);
}
#undef FUNC_NAME


SCM_DEFINE1 (scm_leq_p, "<=", scm_tc7_rpsubr,
             (SCM x, SCM y),
	     "")
#define FUNC_NAME s_scm_leq_p
{
  return SCM_BOOL_NOT (scm_less_p (y, x));
}
#undef FUNC_NAME


SCM_DEFINE1 (scm_geq_p, ">=", scm_tc7_rpsubr,
             (SCM x, SCM y),
	     "")
#define FUNC_NAME s_scm_geq_p
{
  return SCM_BOOL_NOT (scm_less_p (x, y));
}
#undef FUNC_NAME


SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p);

SCM
scm_zero_p (SCM z)
{
#ifdef SCM_FLOATS
  if (SCM_NINUMP (z))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (z), badz);
      if (SCM_BIGP (z))
	return SCM_BOOL_F;
      if (!SCM_INEXP (z))
	{
	badz:
	  SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p);
	}
#else
      SCM_GASSERT1 (SCM_INEXP (z),
		    g_zero_p, z, SCM_ARG1, s_zero_p);
#endif
      return SCM_BOOL(z == scm_flo0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (z))
    {
      SCM_GASSERT1 (SCM_BIGP (z),
		    g_zero_p, z, SCM_ARG1, s_zero_p);
      return SCM_BOOL_F;
    }
#else
  SCM_GASSERT1 (SCM_INUMP (z), g_zero_p, z, SCM_ARG1, s_zero_p);
#endif
#endif
  return SCM_BOOL(z == SCM_INUM0);
}


SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p);

SCM
scm_positive_p (SCM x)
{
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (x), badx);
      if (SCM_BIGP (x))
	return SCM_BOOL(SCM_TYP16 (x) == scm_tc16_bigpos);
      if (!SCM_REALP (x))
	{
	badx:
	  SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p);
	}
#else
      SCM_GASSERT1 (SCM_REALP (x),
		    g_positive_p, x, SCM_ARG1, s_positive_p);
#endif
      return SCM_BOOL(SCM_REALPART (x) > 0.0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT1 (SCM_BIGP (x),
		    g_positive_p, x, SCM_ARG1, s_positive_p);
      return SCM_BOOL(SCM_TYP16 (x) == scm_tc16_bigpos);
    }
#else
  SCM_GASSERT1 (SCM_INUMP (x), g_positive_p, x, SCM_ARG1, s_positive_p);
#endif
#endif
  return SCM_BOOL(x > SCM_INUM0);
}


SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p);

SCM
scm_negative_p (SCM x)
{
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (x), badx);
      if (SCM_BIGP (x))
	return SCM_NEGATE_BOOL(SCM_TYP16 (x) == scm_tc16_bigpos);
      if (!(SCM_REALP (x)))
	{
	badx:
	  SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p);
	}
#else
      SCM_GASSERT1 (SCM_REALP (x),
		    g_negative_p, x, SCM_ARG1, s_negative_p);
#endif
      return SCM_BOOL(SCM_REALPART (x) < 0.0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT1 (SCM_BIGP (x),
		    g_negative_p, x, SCM_ARG1, s_negative_p);
      return SCM_BOOL(SCM_TYP16 (x) == scm_tc16_bigneg);
    }
#else
  SCM_GASSERT1 (SCM_INUMP (x), g_negative_p, x, SCM_ARG1, s_negative_p);
#endif
#endif
  return SCM_BOOL(x < SCM_INUM0);
}


SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max);

SCM
scm_max (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  double z;
#endif
  if (SCM_UNBNDP (y))
    {
      SCM_GASSERT0 (!SCM_UNBNDP (x),
		    g_max, scm_makfrom0str (s_max), SCM_WNA, 0);
      SCM_GASSERT1 (SCM_NUMBERP (x), g_max, x, SCM_ARG1, s_max);
      return x;
    }
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx2:
	  SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    return SCM_BIGSIGN (x) ? y : x;
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    return (1 == scm_bigcomp (x, y)) ? y : x;
	  SCM_ASRTGO (SCM_REALP (y), bady);
	  z = scm_big2dbl (x);
	  return (z < SCM_REALPART (y)) ? y : scm_makdbl (z, 0.0);
	}
      SCM_ASRTGO (SCM_REALP (x), badx2);
#else
      SCM_GASSERT2 (SCM_REALP (x),
		    g_max, x, y, SCM_ARG1, s_max);
#endif
      if (SCM_INUMP (y))
	return ((SCM_REALPART (x) < (z = SCM_INUM (y)))
		? scm_makdbl (z, 0.0)
		: x);
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return ((SCM_REALPART (x) < (z = scm_big2dbl (y)))
		? scm_makdbl (z, 0.0)
		: x);
      SCM_ASRTGO (SCM_REALP (y), bady);
#else
      SCM_ASRTGO (SCM_REALP (y), bady);
#endif
      return (SCM_REALPART (x) < SCM_REALPART (y)) ? y : x;
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return SCM_BIGSIGN (y) ? x : y;
      if (!(SCM_REALP (y)))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
	}
#else
      if (!SCM_REALP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
	}
#endif
      return (((z = SCM_INUM (x)) < SCM_REALPART (y))
	      ? y
	      : scm_makdbl (z, 0.0));
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_max, x, y, SCM_ARG1, s_max);
      if (SCM_INUMP (y))
	return SCM_BIGSIGN (x) ? y : x;
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return (1 == scm_bigcomp (x, y)) ? y : x;
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
	}
      return SCM_BIGSIGN (y) ? x : y;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_max, x, y, SCM_ARG1, s_max);
  SCM_GASSERT2 (SCM_INUMP (y), g_max, x, y, SCM_ARGn, s_max);
#endif
#endif
  return ((long) x < (long) y) ? y : x;
}


SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min);

SCM
scm_min (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  double z;
#endif
  if (SCM_UNBNDP (y))
    {
      SCM_GASSERT0 (!SCM_UNBNDP (x),
		    g_min, scm_makfrom0str (s_min), SCM_WNA, 0);
      SCM_GASSERT1 (SCM_NUMBERP (x), g_min, x, SCM_ARG1, s_min);
      return x;
    }
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx2:
	  SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    return SCM_BIGSIGN (x) ? x : y;
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    return (-1 == scm_bigcomp (x, y)) ? y : x;
	  SCM_ASRTGO (SCM_REALP (y), bady);
	  z = scm_big2dbl (x);
	  return (z > SCM_REALPART (y)) ? y : scm_makdbl (z, 0.0);
	}
      SCM_ASRTGO (SCM_REALP (x), badx2);
#else
      SCM_GASSERT2 (SCM_REALP (x),
		    g_min, x, y, SCM_ARG1, s_min);
#endif
      if (SCM_INUMP (y))
	return ((SCM_REALPART (x) > (z = SCM_INUM (y)))
		? scm_makdbl (z, 0.0)
		: x);
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return ((SCM_REALPART (x) > (z = scm_big2dbl (y)))
		? scm_makdbl (z, 0.0)
		: x);
      SCM_ASRTGO (SCM_REALP (y), bady);
#else
      SCM_ASRTGO (SCM_REALP (y), bady);
#endif
      return (SCM_REALPART (x) > SCM_REALPART (y)) ? y : x;
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return SCM_BIGSIGN (y) ? y : x;
      if (!(SCM_REALP (y)))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
	}
#else
      if (!SCM_REALP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
	}
#endif
      return (((z = SCM_INUM (x)) > SCM_REALPART (y))
	      ? y
	      : scm_makdbl (z, 0.0));
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_min, x, y, SCM_ARG1, s_min);
      if (SCM_INUMP (y))
	return SCM_BIGSIGN (x) ? x : y;
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return (-1 == scm_bigcomp (x, y)) ? y : x;
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
	}
      return SCM_BIGSIGN (y) ? y : x;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_min, x, y, SCM_ARG1, s_min);
  SCM_GASSERT2 (SCM_INUMP (y), g_min, x, y, SCM_ARGn, s_min);
#endif
#endif
  return ((long) x > (long) y) ? y : x;
}


SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum);

SCM
scm_sum (SCM x, SCM y)
{
  if (SCM_UNBNDP (y))
    {
      if (SCM_UNBNDP (x))
	return SCM_INUM0;
      SCM_GASSERT1 (SCM_NUMBERP (x), g_sum, x, SCM_ARG1, s_sum);
      return x;
    }
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
      SCM t;
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx2:
	  SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    {
	      t = x;
	      x = y;
	      y = t;
	      goto intbig;
	    }
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    {
	      if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y))
		{
		  t = x;
		  x = y;
		  y = t;
		}
	      return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				 SCM_BIGSIGN (x),
				 y, 0);
	    }
	  SCM_ASRTGO (SCM_INEXP (y), bady);
	bigreal:
	  return scm_makdbl (scm_big2dbl (x) + SCM_REALPART (y),
			     SCM_CPLXP (y) ? SCM_IMAG (y) : 0.0);
	}
      SCM_ASRTGO (SCM_INEXP (x), badx2);
#else
      SCM_ASRTGO (SCM_INEXP (x), badx2);
#endif
      if (SCM_INUMP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto intreal;
	}
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto bigreal;
	}
      else if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
	}
#else
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
	}
#endif
      {
	double i = 0.0;
	if (SCM_CPLXP (x))
	  i = SCM_IMAG (x);
	if (SCM_CPLXP (y))
	  i += SCM_IMAG (y);
	return scm_makdbl (SCM_REALPART (x) + SCM_REALPART (y), i);
      }
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	intbig:
	  {
#ifndef SCM_DIGSTOOBIG
	    long z = scm_pseudolong (SCM_INUM (x));
	    return scm_addbig ((SCM_BIGDIG *) & z,
			       SCM_DIGSPERLONG,
			       (x < 0) ? 0x0100 : 0,
			       y, 0);
#else
	    SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	    scm_longdigs (SCM_INUM (x), zdigs);
	    return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0,
			       y, 0);
#endif
	  }
	}
      SCM_ASRTGO (SCM_INEXP (y), bady);
#else
      SCM_ASRTGO (SCM_INEXP (y), bady);
#endif
    intreal:
      return scm_makdbl (SCM_INUM (x) + SCM_REALPART (y),
			 SCM_CPLXP (y) ? SCM_IMAG (y) : 0.0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM t;
      SCM_ASRTGO (SCM_BIGP (x), badx2);
      if (SCM_INUMP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto intbig;
	}
      SCM_ASRTGO (SCM_BIGP (y), bady);
      if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y))
	{
	  t = x;
	  x = y;
	  y = t;
	}
      return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), SCM_BIGSIGN (x),
			 y, 0);
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
	}
    intbig:
      {
#ifndef SCM_DIGSTOOBIG
	long z = scm_pseudolong (SCM_INUM (x));
	return scm_addbig (&z, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, y, 0);
#else
	SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	scm_longdigs (SCM_INUM (x), zdigs);
	return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, y, 0);
#endif
      }
    }
#else
  SCM_ASRTGO (SCM_INUMP (x), badx2);
  SCM_GASSERT2 (SCM_INUMP (y), g_sum, x, y, SCM_ARGn, s_sum);
#endif
#endif
  x = SCM_INUM (x) + SCM_INUM (y);
  if (SCM_FIXABLE (x))
    return SCM_MAKINUM (x);
#ifdef SCM_BIGDIG
  return scm_long2big (x);
#else
#ifdef SCM_FLOATS
  return scm_makdbl ((double) x, 0.0);
#else
  scm_num_overflow (s_sum);
  return SCM_UNSPECIFIED;
#endif
#endif
}


SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference);

SCM
scm_difference (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
      if (!(SCM_NIMP (x)))
	{
	  if (SCM_UNBNDP (y))
	    {
	      SCM_GASSERT0 (!SCM_UNBNDP (x), g_difference,
			    scm_makfrom0str (s_difference), SCM_WNA, 0);
	    badx:
	      SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference);
	    }
	  else
	    {
	    badx2:
	      SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference);
	    }
	}
      if (SCM_UNBNDP (y))
	{
#ifdef SCM_BIGDIG
	  if (SCM_BIGP (x))
	    {
	      x = scm_copybig (x, !SCM_BIGSIGN (x));
	      return (SCM_NUMDIGS (x) * SCM_BITSPERDIG / SCM_CHAR_BIT
		      <= sizeof (SCM)
		      ? scm_big2inum (x, SCM_NUMDIGS (x))
		      : x);
	    }
#endif
	  SCM_ASRTGO (SCM_INEXP (x), badx);
	  return scm_makdbl (- SCM_REALPART (x),
			     SCM_CPLXP (x) ? -SCM_IMAG (x) : 0.0);
	}
      if (SCM_INUMP (y))
	return scm_sum (x, SCM_MAKINUM (- SCM_INUM (y)));
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (x))
	{
	  if (SCM_BIGP (y))
	    return ((SCM_NUMDIGS (x) < SCM_NUMDIGS (y))
		    ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				  SCM_BIGSIGN (x),
				  y, 0x0100)
		    : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y),
				  SCM_BIGSIGN (y) ^ 0x0100,
				  x, 0));
	  SCM_ASRTGO (SCM_INEXP (y), bady);
	  return scm_makdbl (scm_big2dbl (x) - SCM_REALPART (y),
			     SCM_CPLXP (y) ? -SCM_IMAG (y) : 0.0);
	}
      SCM_ASRTGO (SCM_INEXP (x), badx2);
      if (SCM_BIGP (y))
	return scm_makdbl (SCM_REALPART (x) - scm_big2dbl (y),
			   SCM_CPLXP (x) ? SCM_IMAG (x) : 0.0);
      SCM_ASRTGO (SCM_INEXP (y), bady);
#else
      SCM_ASRTGO (SCM_INEXP (x), badx2);
      SCM_ASRTGO (SCM_INEXP (y), bady);
#endif
      if (SCM_CPLXP (x))
	{
	  if (SCM_CPLXP (y))
	    return scm_makdbl (SCM_REAL (x) - SCM_REAL (y),
			       SCM_IMAG (x) - SCM_IMAG (y));
	  else
	    return scm_makdbl (SCM_REAL (x) - SCM_REALPART (y), SCM_IMAG (x));
	}
      return scm_makdbl (SCM_REALPART (x) - SCM_REALPART (y),
			 SCM_CPLXP (y) ? - SCM_IMAG (y) : 0.0);
    }
  if (SCM_UNBNDP (y))
    {
      x = -SCM_INUM (x);
      goto checkx;
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
#ifndef SCM_DIGSTOOBIG
	  long z = scm_pseudolong (SCM_INUM (x));
	  return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
			     (x < 0) ? 0x0100 : 0,
			     y, 0x0100);
#else
	  SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	  scm_longdigs (SCM_INUM (x), zdigs);
	  return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0,
			     y, 0x0100);
#endif
	}
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
	}
#else
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
	}
#endif
      return scm_makdbl (SCM_INUM (x) - SCM_REALPART (y),
			 SCM_CPLXP (y) ? -SCM_IMAG (y) : 0.0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_difference, x, y, SCM_ARG1, s_difference);
      if (SCM_UNBNDP (y))
	{
	  x = scm_copybig (x, !SCM_BIGSIGN (x));
	  return (SCM_NUMDIGS (x) * SCM_BITSPERDIG / SCM_CHAR_BIT
		  <= sizeof (SCM)
		  ? scm_big2inum (x, SCM_NUMDIGS (x))
		  : x);
	}
      if (SCM_INUMP (y))
	{
#ifndef SCM_DIGSTOOBIG
	  long z = scm_pseudolong (SCM_INUM (y));
	  return scm_addbig (&z, SCM_DIGSPERLONG, (y < 0) ? 0 : 0x0100, x, 0);
#else
	  SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	  scm_longdigs (SCM_INUM (x), zdigs);
	  return scm_addbig (zdigs, SCM_DIGSPERLONG, (y < 0) ? 0 : 0x0100,
			     x, 0);
#endif
	}
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) ?
	scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), SCM_BIGSIGN (x),
		    y, 0x0100) :
	scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), SCM_BIGSIGN (y) ^ 0x0100,
		    x, 0);
    }
  if (SCM_UNBNDP (y))
    {
      x = -SCM_INUM (x);
      goto checkx;
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
	}
      {
#ifndef SCM_DIGSTOOBIG
	long z = scm_pseudolong (SCM_INUM (x));
	return scm_addbig (&z, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0,
			   y, 0x0100);
#else
	SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	scm_longdigs (SCM_INUM (x), zdigs);
	return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0,
			   y, 0x0100);
#endif
      }
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_difference, x, y, SCM_ARG1, s_difference);
  if (SCM_UNBNDP (y))
    {
      x = -SCM_INUM (x);
      goto checkx;
    }
  SCM_GASSERT2 (SCM_INUMP (y), g_difference, x, y, SCM_ARGn, s_difference);
#endif
#endif
  x = SCM_INUM (x) - SCM_INUM (y);
 checkx:
  if (SCM_FIXABLE (x))
    return SCM_MAKINUM (x);
#ifdef SCM_BIGDIG
  return scm_long2big (x);
#else
#ifdef SCM_FLOATS
  return scm_makdbl ((double) x, 0.0);
#else
  scm_num_overflow (s_difference);
  return SCM_UNSPECIFIED;
#endif
#endif
}


SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product);

SCM
scm_product (SCM x, SCM y)
{
  if (SCM_UNBNDP (y))
    {
      if (SCM_UNBNDP (x))
	return SCM_MAKINUM (1L);
      SCM_GASSERT1 (SCM_NUMBERP (x), g_product, x, SCM_ARG1, s_product);
      return x;
    }
#ifdef SCM_FLOATS
  if (SCM_NINUMP (x))
    {
      SCM t;
#ifdef SCM_BIGDIG
      if (!SCM_NIMP (x))
	{
	badx2:
	  SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product);
	}
      if (SCM_BIGP (x))
	{
	  if (SCM_INUMP (y))
	    {
	      t = x;
	      x = y;
	      y = t;
	      goto intbig;
	    }
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			       SCM_BDIGITS (y), SCM_NUMDIGS (y),
			       SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y));
	  SCM_ASRTGO (SCM_INEXP (y), bady);
	bigreal:
	  {
	    double bg = scm_big2dbl (x);
	    return scm_makdbl (bg * SCM_REALPART (y),
			       SCM_CPLXP (y) ? bg * SCM_IMAG (y) : 0.0);
	  }
	}
      SCM_ASRTGO (SCM_INEXP (x), badx2);
#else
      SCM_ASRTGO (SCM_INEXP (x), badx2);
#endif
      if (SCM_INUMP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto intreal;
	}
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	  t = x;
	  x = y;
	  y = t;
	  goto bigreal;
	}
      else if (!(SCM_INEXP (y)))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
	}
#else
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
	}
#endif
      if (SCM_CPLXP (x))
	{
	  if (SCM_CPLXP (y))
	    return scm_makdbl (SCM_REAL (x) * SCM_REAL (y)
			       - SCM_IMAG (x) * SCM_IMAG (y),
			       SCM_REAL (x) * SCM_IMAG (y)
			       + SCM_IMAG (x) * SCM_REAL (y));
	  else
	    return scm_makdbl (SCM_REAL (x) * SCM_REALPART (y),
			       SCM_IMAG (x) * SCM_REALPART (y));
	}
      return scm_makdbl (SCM_REALPART (x) * SCM_REALPART (y),
			 SCM_CPLXP (y)
			 ? SCM_REALPART (x) * SCM_IMAG (y)
			 : 0.0);
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	intbig:
	  if (SCM_INUM0 == x)
	    return x;
	  if (SCM_MAKINUM (1L) == x)
	    return y;
	  {
#ifndef SCM_DIGSTOOBIG
	    long z = scm_pseudolong (SCM_INUM (x));
	    return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
			       SCM_BDIGITS (y), SCM_NUMDIGS (y),
			       SCM_BIGSIGN (y) ? (x > 0) : (x < 0));
#else
	    SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	    scm_longdigs (SCM_INUM (x), zdigs);
	    return scm_mulbig (zdigs, SCM_DIGSPERLONG,
			       SCM_BDIGITS (y), SCM_NUMDIGS (y),
			       SCM_BIGSIGN (y) ? (x > 0) : (x < 0));
#endif
	  }
	}
      SCM_ASRTGO (SCM_INEXP (y), bady);
#else
      SCM_ASRTGO (SCM_INEXP (y), bady);
#endif
    intreal:
      return scm_makdbl (SCM_INUM (x) * SCM_REALPART (y),
			 SCM_CPLXP (y) ? SCM_INUM (x) * SCM_IMAG (y) : 0.0);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM_ASRTGO (SCM_BIGP (x), badx2);
      if (SCM_INUMP (y))
	{
	  SCM t = x;
	  x = y;
	  y = t;
	  goto intbig;
	}
      SCM_ASRTGO (SCM_BIGP (y), bady);
      return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			 SCM_BDIGITS (y), SCM_NUMDIGS (y),
			 SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y));
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
	}
    intbig:
      if (SCM_INUM0 == x)
	return x;
      if (SCM_MAKINUM (1L) == x)
	return y;
      {
#ifndef SCM_DIGSTOOBIG
	long z = scm_pseudolong (SCM_INUM (x));
	return scm_mulbig (&z, SCM_DIGSPERLONG,
			   SCM_BDIGITS (y), SCM_NUMDIGS (y),
			   SCM_BIGSIGN (y) ? (x > 0) : (x < 0));
#else
	SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	scm_longdigs (SCM_INUM (x), zdigs);
	return scm_mulbig (zdigs, SCM_DIGSPERLONG,
			   SCM_BDIGITS (y), SCM_NUMDIGS (y),
			   SCM_BIGSIGN (y) ? (x > 0) : (x < 0));
#endif
      }
    }
#else
  SCM_ASRTGO (SCM_INUMP (x), badx2);
  SCM_GASSERT (SCM_INUMP (y), g_product, x, y, SCM_ARGn, s_product);
#endif
#endif
  {
    long i, j, k;
    i = SCM_INUM (x);
    if (0 == i)
      return x;
    j = SCM_INUM (y);
    k = i * j;
    y = SCM_MAKINUM (k);
    if (k != SCM_INUM (y) || k / i != j)
#ifdef SCM_BIGDIG
      {
	int sgn = (i < 0) ^ (j < 0);
#ifndef SCM_DIGSTOOBIG
	i = scm_pseudolong (i);
	j = scm_pseudolong (j);
	return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG,
			   (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn);
#else /* SCM_DIGSTOOBIG */
	SCM_BIGDIG idigs[SCM_DIGSPERLONG];
	SCM_BIGDIG jdigs[SCM_DIGSPERLONG];
	scm_longdigs (i, idigs);
	scm_longdigs (j, jdigs);
	return scm_mulbig (idigs, SCM_DIGSPERLONG,
			   jdigs, SCM_DIGSPERLONG,
			   sgn);
#endif
      }
#else
#ifdef SCM_FLOATS
    return scm_makdbl (((double) i) * ((double) j), 0.0);
#else
    scm_num_overflow (s_product);
#endif
#endif
    return y;
  }
}


double
scm_num2dbl (SCM a, const char *why)
{
  if (SCM_INUMP (a))
    return (double) SCM_INUM (a);
#ifdef SCM_FLOATS
  SCM_ASSERT (SCM_NIMP (a), a, "wrong type argument", why);
  if (SCM_REALP (a))
    return (SCM_REALPART (a));
#endif
#ifdef SCM_BIGDIG
  return scm_big2dbl (a);
#endif
  SCM_ASSERT (0, a, "wrong type argument", why);
  return SCM_UNSPECIFIED;
}


SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide);

SCM
scm_divide (SCM x, SCM y)
{
#ifdef SCM_FLOATS
  double d, r, i, a;
  if (SCM_NINUMP (x))
    {
      if (!(SCM_NIMP (x)))
	{
	  if (SCM_UNBNDP (y))
	    {
	      SCM_GASSERT0 (!SCM_UNBNDP (x),
			    g_divide, scm_makfrom0str (s_divide), SCM_WNA, 0);
	    badx:
	      SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
	    }
	  else
	    {
	    badx2:
	      SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide);
	    }
	}
      if (SCM_UNBNDP (y))
	{
#ifdef SCM_BIGDIG
	  if (SCM_BIGP (x))
	    return scm_makdbl (1.0 / scm_big2dbl (x), 0.0);
#endif
	  SCM_ASRTGO (SCM_INEXP (x), badx);
	  if (SCM_REALP (x))
	    return scm_makdbl (1.0 / SCM_REALPART (x), 0.0);
	  r = SCM_REAL (x);
	  i = SCM_IMAG (x);
	  d = r * r + i * i;
	  return scm_makdbl (r / d, -i / d);
	}
#ifdef SCM_BIGDIG
      if (SCM_BIGP (x))
	{
	  SCM z;
	  if (SCM_INUMP (y))
	    {
	      z = SCM_INUM (y);
#ifndef SCM_RECKLESS
	      if (!z)
		scm_num_overflow (s_divide);
#endif
	      if (1 == z)
		return x;
	      if (z < 0)
		z = -z;
	      if (z < SCM_BIGRAD)
		{
		  SCM w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0));
		  return (scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w),
					 (SCM_BIGDIG) z)
			  ? scm_makdbl (scm_big2dbl (x) / SCM_INUM (y), 0.0)
			  : scm_normbig (w));
		}
#ifndef SCM_DIGSTOOBIG
	      z = scm_pseudolong (z);
	      z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				 (SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
				 SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3);
#else
	      {
		SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
		scm_longdigs (z, zdigs);
		z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				   zdigs, SCM_DIGSPERLONG,
				   SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3);
	      }
#endif
	      return z ? z : scm_makdbl (scm_big2dbl (x) / SCM_INUM (y), 0.0);
	    }
	  SCM_ASRTGO (SCM_NIMP (y), bady);
	  if (SCM_BIGP (y))
	    {
	      z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
				 SCM_BDIGITS (y), SCM_NUMDIGS (y),
				 SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3);
	      return z ? z : scm_makdbl (scm_big2dbl (x) / scm_big2dbl (y),
					 0.0);
	    }
	  SCM_ASRTGO (SCM_INEXP (y), bady);
	  if (SCM_REALP (y))
	    return scm_makdbl (scm_big2dbl (x) / SCM_REALPART (y), 0.0);
	  a = scm_big2dbl (x);
	  goto complex_div;
	}
#endif
      SCM_ASRTGO (SCM_INEXP (x), badx2);
      if (SCM_INUMP (y))
	{
	  d = SCM_INUM (y);
	  goto basic_div;
	}
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	{
	  d = scm_big2dbl (y);
	  goto basic_div;
	}
      SCM_ASRTGO (SCM_INEXP (y), bady);
#else
      SCM_ASRTGO (SCM_INEXP (y), bady);
#endif
      if (SCM_REALP (y))
	{
	  d = SCM_REALPART (y);
	basic_div:
	  return scm_makdbl (SCM_REALPART (x) / d,
			     SCM_CPLXP (x) ? SCM_IMAG (x) / d : 0.0);
	}
      a = SCM_REALPART (x);
      if (SCM_REALP (x))
	goto complex_div;
      r = SCM_REAL (y);
      i = SCM_IMAG (y);
      d = r * r + i * i;
      return scm_makdbl ((a * r + SCM_IMAG (x) * i) / d,
			 (SCM_IMAG (x) * r - a * i) / d);
    }
  if (SCM_UNBNDP (y))
    {
      if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x))
	return x;
      return scm_makdbl (1.0 / ((double) SCM_INUM (x)), 0.0);
    }
  if (SCM_NINUMP (y))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (y), bady);
      if (SCM_BIGP (y))
	return scm_makdbl (SCM_INUM (x) / scm_big2dbl (y), 0.0);
      if (!(SCM_INEXP (y)))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
	}
#else
      if (!SCM_INEXP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
	}
#endif
      if (SCM_REALP (y))
	return scm_makdbl (SCM_INUM (x) / SCM_REALPART (y), 0.0);
      a = SCM_INUM (x);
    complex_div:
      r = SCM_REAL (y);
      i = SCM_IMAG (y);
      d = r * r + i * i;
      return scm_makdbl ((a * r) / d, (-a * i) / d);
    }
#else
#ifdef SCM_BIGDIG
  if (SCM_NINUMP (x))
    {
      SCM z;
      SCM_GASSERT2 (SCM_BIGP (x),
		    g_divide, x, y, SCM_ARG1, s_divide);
      if (SCM_UNBNDP (y))
	goto ov;
      if (SCM_INUMP (y))
	{
	  z = SCM_INUM (y);
	  if (!z)
	    goto ov;
	  if (1 == z)
	    return x;
	  if (z < 0)
	    z = -z;
	  if (z < SCM_BIGRAD)
	    {
	      SCM w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0));
	      if (scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w),
				 (SCM_BIGDIG) z))
		goto ov;
	      return w;
	    }
#ifndef SCM_DIGSTOOBIG
	  z = scm_pseudolong (z);
	  z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			     &z, SCM_DIGSPERLONG,
			     SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3);
#else
	  {
	    SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
	    scm_longdigs (z, zdigs);
	    z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			       zdigs, SCM_DIGSPERLONG,
			       SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3);
	  }
#endif
	}
      else
	{
	  SCM_ASRTGO (SCM_BIGP (y), bady);
	  z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
			     SCM_BDIGITS (y), SCM_NUMDIGS (y),
			     SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3);
	}
      if (!z)
	goto ov;
      return z;
    }
  if (SCM_UNBNDP (y))
    {
      if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x))
	return x;
      goto ov;
    }
  if (SCM_NINUMP (y))
    {
      if (!SCM_BIGP (y))
	{
	bady:
	  SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
	}
      goto ov;
    }
#else
  SCM_GASSERT2 (SCM_INUMP (x), g_divide, x, y, SCM_ARG1, s_divide);
  if (SCM_UNBNDP (y))
    {
      if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x))
	return x;
      goto ov;
    }
  SCM_GASSERT2 (SCM_INUMP (y), g_divide, x, y, SCM_ARGn, s_divide);
#endif
#endif
  {
    long z = SCM_INUM (y);
    if ((0 == z) || SCM_INUM (x) % z)
      goto ov;
    z = SCM_INUM (x) / z;
    if (SCM_FIXABLE (z))
      return SCM_MAKINUM (z);
#ifdef SCM_BIGDIG
    return scm_long2big (z);
#endif
#ifdef SCM_FLOATS
  ov:
    return scm_makdbl (((double) SCM_INUM (x)) / ((double) SCM_INUM (y)), 0.0);
#else
  ov:
    scm_num_overflow (s_divide);
    return SCM_UNSPECIFIED;
#endif
  }
}


#ifdef SCM_FLOATS
SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh);

double
scm_asinh (double x)
{
  return log (x + sqrt (x * x + 1));
}


SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh);

double
scm_acosh (double x)
{
  return log (x + sqrt (x * x - 1));
}


SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh);

double
scm_atanh (double x)
{
  return 0.5 * log ((1 + x) / (1 - x));
}


SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate);

double
scm_truncate (double x)
{
  if (x < 0.0)
    return -floor (-x);
  return floor (x);
}


SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round);

double
scm_round (double x)
{
  double plus_half = x + 0.5;
  double result = floor (plus_half);
  /* Adjust so that the scm_round is towards even.  */
  return (plus_half == result && plus_half / 2 != floor (plus_half / 2))
    ? result - 1 : result;
}


SCM_GPROC1 (s_exact_to_inexact, "exact->inexact", scm_tc7_cxr, (SCM (*)()) scm_exact_to_inexact, g_exact_to_inexact);

double
scm_exact_to_inexact (double z)
{
  return z;
}


SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor);
SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil);
SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt);
SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs);
SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp);
SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log);
SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin);
SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos);
SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan);
SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin);
SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos);
SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan);
SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh);
SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh);
SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh);

struct dpair
{
  double x, y;
};

static void scm_two_doubles (SCM z1,
			     SCM z2,
			     const char *sstring,
			     struct dpair * xy);

static void
scm_two_doubles (SCM z1, SCM z2, const char *sstring, struct dpair *xy)
{
  if (SCM_INUMP (z1))
    xy->x = SCM_INUM (z1);
  else
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (z1), badz1);
      if (SCM_BIGP (z1))
	xy->x = scm_big2dbl (z1);
      else
	{
#ifndef SCM_RECKLESS
	  if (!SCM_REALP (z1))
	    badz1:scm_wta (z1, (char *) SCM_ARG1, sstring);
#endif
	  xy->x = SCM_REALPART (z1);
	}
#else
      {
	SCM_ASSERT (SCM_REALP (z1), z1, SCM_ARG1, sstring);
	xy->x = SCM_REALPART (z1);
      }
#endif
    }
  if (SCM_INUMP (z2))
    xy->y = SCM_INUM (z2);
  else
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (z2), badz2);
      if (SCM_BIGP (z2))
	xy->y = scm_big2dbl (z2);
      else
	{
#ifndef SCM_RECKLESS
	  if (!(SCM_REALP (z2)))
	    badz2:scm_wta (z2, (char *) SCM_ARG2, sstring);
#endif
	  xy->y = SCM_REALPART (z2);
	}
#else
      {
	SCM_ASSERT (SCM_REALP (z2), z2, SCM_ARG2, sstring);
	xy->y = SCM_REALPART (z2);
      }
#endif
    }
}


SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0,
            (SCM z1, SCM z2),
	    "")
#define FUNC_NAME s_scm_sys_expt
{
  struct dpair xy;
  scm_two_doubles (z1, z2, FUNC_NAME, &xy);
  return scm_makdbl (pow (xy.x, xy.y), 0.0);
}
#undef FUNC_NAME


SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0,
            (SCM z1, SCM z2),
	    "")
#define FUNC_NAME s_scm_sys_atan2
{
  struct dpair xy;
  scm_two_doubles (z1, z2, FUNC_NAME, &xy);
  return scm_makdbl (atan2 (xy.x, xy.y), 0.0);
}
#undef FUNC_NAME


SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0,
            (SCM z1, SCM z2),
	    "")
#define FUNC_NAME s_scm_make_rectangular
{
  struct dpair xy;
  scm_two_doubles (z1, z2, FUNC_NAME, &xy);
  return scm_makdbl (xy.x, xy.y);
}
#undef FUNC_NAME


SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0,
            (SCM z1, SCM z2),
	    "")
#define FUNC_NAME s_scm_make_polar
{
  struct dpair xy;
  scm_two_doubles (z1, z2, FUNC_NAME, &xy);
  return scm_makdbl (xy.x * cos (xy.y), xy.x * sin (xy.y));
}
#undef FUNC_NAME


SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part);

SCM
scm_real_part (SCM z)
{
  if (SCM_NINUMP (z))
    {
#ifdef SCM_BIGDIG
      SCM_ASRTGO (SCM_NIMP (z), badz);
      if (SCM_BIGP (z))
	return z;
      if (!(SCM_INEXP (z)))
	{
	badz:
	  SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part);
	}
#else
      SCM_GASSERT1 (SCM_INEXP (z),
		    g_real_part, z, SCM_ARG1, s_real_part);
#endif
      if (SCM_CPLXP (z))
	return scm_makdbl (SCM_REAL (z), 0.0);
    }
  return z;
}


SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part);

SCM
scm_imag_part (SCM z)
{
  if (SCM_INUMP (z))
    return SCM_INUM0;
#ifdef SCM_BIGDIG
  SCM_ASRTGO (SCM_NIMP (z), badz);
  if (SCM_BIGP (z))
    return SCM_INUM0;
  if (!(SCM_INEXP (z)))
    {
    badz:
      SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part);
    }
#else
  SCM_GASSERT1 (SCM_INEXP (z),
		g_imag_part, z, SCM_ARG1, s_imag_part);
#endif
  if (SCM_CPLXP (z))
    return scm_makdbl (SCM_IMAG (z), 0.0);
  return scm_flo0;
}


SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude);

SCM
scm_magnitude (SCM z)
{
  if (SCM_INUMP (z))
    return scm_abs (z);
#ifdef SCM_BIGDIG
  SCM_ASRTGO (SCM_NIMP (z), badz);
  if (SCM_BIGP (z))
    return scm_abs (z);
  if (!(SCM_INEXP (z)))
    {
    badz:
      SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude);
    }
#else
  SCM_GASSERT1 (SCM_INEXP (z),
		g_magnitude, z, SCM_ARG1, s_magnitude);
#endif
  if (SCM_CPLXP (z))
    {
      double i = SCM_IMAG (z), r = SCM_REAL (z);
      return scm_makdbl (sqrt (i * i + r * r), 0.0);
    }
  return scm_makdbl (fabs (SCM_REALPART (z)), 0.0);
}


SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle);

SCM
scm_angle (SCM z)
{
  double x, y = 0.0;
  if (SCM_INUMP (z))
    {
      x = (z >= SCM_INUM0) ? 1.0 : -1.0;
      goto do_angle;
    }
#ifdef SCM_BIGDIG
  SCM_ASRTGO (SCM_NIMP (z), badz);
  if (SCM_BIGP (z))
    {
      x = (SCM_TYP16 (z) == scm_tc16_bigpos) ? 1.0 : -1.0;
      goto do_angle;
    }
  if (!(SCM_INEXP (z)))
    {
    badz:
      SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle);
    }
#else
  SCM_GASSERT1 (SCM_INEXP (z), g_angle, z, SCM_ARG1, s_angle);
#endif
  if (SCM_REALP (z))
    {
      x = SCM_REALPART (z);
      goto do_angle;
    }
  x = SCM_REAL (z);
  y = SCM_IMAG (z);
 do_angle:
  return scm_makdbl (atan2 (y, x), 0.0);
}


SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, 
            (SCM z),
	    "")
#define FUNC_NAME s_scm_inexact_to_exact
{
  if (SCM_INUMP (z))
    return z;
#ifdef SCM_BIGDIG
  SCM_ASRTGO (SCM_NIMP (z), badz);
  if (SCM_BIGP (z))
    return z;
#ifndef SCM_RECKLESS
  if (!(SCM_REALP (z)))
    {
    badz:
      SCM_WTA (1, z);
    }
#endif
#else
  SCM_VALIDATE_REAL (1,z);
#endif
#ifdef SCM_BIGDIG
  {
    double u = floor (SCM_REALPART (z) + 0.5);
    if ((u <= SCM_MOST_POSITIVE_FIXNUM) && (-u <= -SCM_MOST_NEGATIVE_FIXNUM))
      {
	/* Negation is a workaround for HP700 cc bug */
	SCM ans = SCM_MAKINUM ((long) u);
	if (SCM_INUM (ans) == (long) u)
	  return ans;
      }
    SCM_ASRTGO (isfinite (u), badz);	/* problem? */
    return scm_dbl2big (u);
  }
#else
  return SCM_MAKINUM ((long) floor (SCM_REALPART (z) + 0.5));
#endif
}
#undef FUNC_NAME


#else /* ~SCM_FLOATS */
SCM_GPROC (s_trunc, "truncate", 1, 0, 0, scm_trunc, g_trunc);

SCM
scm_trunc (SCM x)
{
  SCM_GASSERT2 (SCM_INUMP (x), g_trunc, x, y, SCM_ARG1, s_truncate);
  return x;
}


#endif /* SCM_FLOATS */

#ifdef SCM_BIGDIG
#ifdef SCM_FLOATS
/* d must be integer */

SCM
scm_dbl2big (double d)
{
  scm_sizet i = 0;
  long c;
  SCM_BIGDIG *digits;
  SCM ans;
  double u = (d < 0) ? -d : d;
  while (0 != floor (u))
    {
      u /= SCM_BIGRAD;
      i++;
    }
  ans = scm_mkbig (i, d < 0);
  digits = SCM_BDIGITS (ans);
  while (i--)
    {
      u *= SCM_BIGRAD;
      c = floor (u);
      u -= c;
      digits[i] = c;
    }
#ifndef SCM_RECKLESS
  if (u != 0)
    scm_num_overflow ("dbl2big");
#endif
  return ans;
}


double
scm_big2dbl (SCM b)
{
  double ans = 0.0;
  scm_sizet i = SCM_NUMDIGS (b);
  SCM_BIGDIG *digits = SCM_BDIGITS (b);
  while (i--)
    ans = digits[i] + SCM_BIGRAD * ans;
  if (scm_tc16_bigneg == SCM_TYP16 (b))
    return -ans;
  return ans;
}
#endif
#endif


SCM
scm_long2num (long sl)
{
  if (!SCM_FIXABLE (sl))
    {
#ifdef SCM_BIGDIG
      return scm_long2big (sl);
#else
#ifdef SCM_FLOATS
      return scm_makdbl ((double) sl, 0.0);
#else
      return SCM_BOOL_F;
#endif
#endif
    }
  return SCM_MAKINUM (sl);
}


#ifdef HAVE_LONG_LONGS

SCM
scm_long_long2num (long_long sl)
{
  if (!SCM_FIXABLE (sl))
    {
#ifdef SCM_BIGDIG
      return scm_long_long2big (sl);
#else
#ifdef SCM_FLOATS
      return scm_makdbl ((double) sl, 0.0);
#else
      return SCM_BOOL_F;
#endif
#endif
    }
  return SCM_MAKINUM (sl);
}
#endif


SCM
scm_ulong2num (unsigned long sl)
{
  if (!SCM_POSFIXABLE (sl))
    {
#ifdef SCM_BIGDIG
      return scm_ulong2big (sl);
#else
#ifdef SCM_FLOATS
      return scm_makdbl ((double) sl, 0.0);
#else
      return SCM_BOOL_F;
#endif
#endif
    }
  return SCM_MAKINUM (sl);
}


long
scm_num2long (SCM num, char *pos, const char *s_caller)
{
  long res;

  if (SCM_INUMP (num))
    {
      res = SCM_INUM (num);
      return res;
    }
  SCM_ASRTGO (SCM_NIMP (num), wrong_type_arg);
#ifdef SCM_FLOATS
  if (SCM_REALP (num))
    {
      volatile double u = SCM_REALPART (num);

      res = u;
      if (res != u)
	goto out_of_range;
      return res;
    }
#endif
#ifdef SCM_BIGDIG
  if (SCM_BIGP (num))
    {
      unsigned long oldres = 0;
      scm_sizet l;
      /* can't use res directly in case num is -2^31.  */
      unsigned long pos_res = 0;

      for (l = SCM_NUMDIGS (num); l--;)
	{
	  pos_res = SCM_BIGUP (pos_res) + SCM_BDIGITS (num)[l];
	  /* check for overflow.  */
	  if (pos_res < oldres) 
	    goto out_of_range;
	  oldres = pos_res;
	}
      if (SCM_TYP16 (num) == scm_tc16_bigpos)
	{
	  res = pos_res;
	  if (res < 0)
	    goto out_of_range;
	}
      else
	{
	  res = -pos_res;
	  if (res > 0)
	    goto out_of_range;
	}
      return res;
    }
#endif
 wrong_type_arg:
  scm_wrong_type_arg (s_caller, (int) pos, num);
 out_of_range:
  scm_out_of_range (s_caller, num);
}


#ifdef HAVE_LONG_LONGS

long_long
scm_num2long_long (SCM num, char *pos, const char *s_caller)
{
  long_long res;

  if (SCM_INUMP (num))
    {
      res = SCM_INUM (num);
      return res;
    }
  SCM_ASRTGO (SCM_NIMP (num), wrong_type_arg);
#ifdef SCM_FLOATS
  if (SCM_REALP (num))
    {
      double u = SCM_REALPART (num);

      res = u;
      if ((res < 0 && u > 0) || (res > 0 && u < 0)) /* check for overflow. */
	goto out_of_range;

      return res;
    }
#endif
#ifdef SCM_BIGDIG
  if (SCM_BIGP (num))
    {
      unsigned long long oldres = 0;
      scm_sizet l;
      /* can't use res directly in case num is -2^63.  */
      unsigned long long pos_res = 0;

      for (l = SCM_NUMDIGS (num); l--;)
	{
	  pos_res = SCM_LONGLONGBIGUP (pos_res) + SCM_BDIGITS (num)[l];
	  /* check for overflow.  */
	  if (pos_res < oldres) 
	    goto out_of_range;
	  oldres = pos_res;
	}
      if (SCM_TYP16 (num) == scm_tc16_bigpos)
	{
	  res = pos_res;
	  if (res < 0)
	    goto out_of_range;
	}
      else
	{
	  res = -pos_res;
	  if (res > 0)
	    goto out_of_range;
	}
      return res;
    }
#endif
 wrong_type_arg:
  scm_wrong_type_arg (s_caller, (int) pos, num);
 out_of_range:
  scm_out_of_range (s_caller, num);
}
#endif


unsigned long
scm_num2ulong (SCM num, char *pos, const char *s_caller)
{
  unsigned long res;

  if (SCM_INUMP (num))
    {
      if (SCM_INUM (num) < 0)
	goto out_of_range;
      res = SCM_INUM (num);
      return res;
    }
  SCM_ASRTGO (SCM_NIMP (num), wrong_type_arg);
#ifdef SCM_FLOATS
  if (SCM_REALP (num))
    {
      double u = SCM_REALPART (num);

      res = u;
      if (res != u)
	goto out_of_range;
      return res;
    }
#endif
#ifdef SCM_BIGDIG
  if (SCM_BIGP (num))
    {
      unsigned long oldres = 0;
      scm_sizet l;

      res = 0;
      for (l = SCM_NUMDIGS (num); l--;)
	{
	  res = SCM_BIGUP (res) + SCM_BDIGITS (num)[l];
	  if (res < oldres)
	    goto out_of_range;
	  oldres = res;
	}
      return res;
    }
#endif
 wrong_type_arg:
  scm_wrong_type_arg (s_caller, (int) pos, num);
 out_of_range:
  scm_out_of_range (s_caller, num);
}


#ifdef SCM_FLOATS
#ifndef DBL_DIG
static void
add1 (double f, double *fsum)
{
  *fsum = f + 1.0;
}
#endif
#endif


void
scm_init_numbers ()
{
  scm_add_feature("complex");
#ifdef SCM_FLOATS
  scm_add_feature("inexact");
#ifdef SCM_SINGLES
  SCM_NEWSMOB(scm_flo0,scm_tc_flo,NULL);
#else
  SCM_NEWSMOB(scm_flo0,scm_tc_dblr,scm_must_malloc (1L * sizeof (double), "real"));
  SCM_REAL (scm_flo0) = 0.0;
#endif
#ifdef DBL_DIG
  scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG;
#else
  {				/* determine floating point precision */
    double f = 0.1;
    double fsum = 1.0 + f;
    while (fsum != 1.0)
      {
	f /= 10.0;
	if (++scm_dblprec > 20)
	  break;
	add1 (f, &fsum);
      }
    scm_dblprec = scm_dblprec - 1;
  }
#endif /* DBL_DIG */
#endif
#include "numbers.x"
}