* .cvsignore: add autom4te.cache and *.c.clean.c.

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

/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001 Free Software Foundation, Inc.
 *
 * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
 * and Bellcore.  See scm_divide.
 *
 *
 * 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.  */

\f

#include <math.h>
#include <ctype.h>
#include "libguile/_scm.h"
#include "libguile/feature.h"
#include "libguile/ports.h"
#include "libguile/root.h"
#include "libguile/smob.h"
#include "libguile/strings.h"

#include "libguile/validate.h"
#include "libguile/numbers.h"
#include "libguile/deprecation.h"

\f

static SCM scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes);
static SCM scm_divbigint (SCM x, long z, int sgn, int mode);


#define SCM_SWAP(x,y) do { SCM __t = x; x = y; y = __t; } while (0)


/* FLOBUFLEN is the maximum number of characters neccessary for the
 * printed or scm_string representation of an inexact number.
 */
#define FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)


/* IS_INF tests its floating point number for infiniteness
   Dirk:FIXME:: This test does not work if x == 0
 */
#ifndef IS_INF
#define IS_INF(x) ((x) == (x) / 2)
#endif


/* Return true if X is not infinite and is not a NaN
   Dirk:FIXME:: Since IS_INF is broken, this test does not work if x == 0
 */
#ifndef isfinite
#define isfinite(x) (!IS_INF (x) && (x) == (x))
#endif

\f

static SCM abs_most_negative_fixnum;

\f


SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, 
            (SCM x),
            "Return @code{#t} if @var{x} is an exact number, @code{#f}\n"
            "otherwise.")
#define FUNC_NAME s_scm_exact_p
{
  if (SCM_INUMP (x)) {
    return SCM_BOOL_T;
  } else if (SCM_BIGP (x)) {
    return SCM_BOOL_T;
  } else {
    return SCM_BOOL_F;
  }
}
#undef FUNC_NAME


SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, 
            (SCM n),
            "Return @code{#t} if @var{n} is an odd number, @code{#f}\n"
            "otherwise.")
#define FUNC_NAME s_scm_odd_p
{
  if (SCM_INUMP (n)) {
    return SCM_BOOL ((4 & SCM_UNPACK (n)) != 0);
  } else if (SCM_BIGP (n)) {
    return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) != 0);
  } else {
    SCM_WRONG_TYPE_ARG (1, n);
  }
}
#undef FUNC_NAME


SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, 
            (SCM n),
            "Return @code{#t} if @var{n} is an even number, @code{#f}\n"
            "otherwise.")
#define FUNC_NAME s_scm_even_p
{
  if (SCM_INUMP (n)) {
    return SCM_BOOL ((4 & SCM_UNPACK (n)) == 0);
  } else if (SCM_BIGP (n)) {
    return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) == 0);
  } else {
    SCM_WRONG_TYPE_ARG (1, n);
  }
}
#undef FUNC_NAME


SCM_GPROC (s_abs, "abs", 1, 0, 0, scm_abs, g_abs);
/* "Return the absolute value of @var{x}."
 */
SCM
scm_abs (SCM x)
{
  if (SCM_INUMP (x)) {
    long int xx = SCM_INUM (x);
    if (xx >= 0) {
      return x;
    } else if (SCM_POSFIXABLE (-xx)) {
      return SCM_MAKINUM (-xx);
    } else {
#ifdef SCM_BIGDIG
      return scm_i_long2big (-xx);
#else
      scm_num_overflow (s_abs);
#endif
    }
  } else if (SCM_BIGP (x)) {
    if (!SCM_BIGSIGN (x)) {
      return x;
    } else {
      return scm_i_copybig (x, 0);
    }
  } else if (SCM_REALP (x)) {
    return scm_make_real (fabs (SCM_REAL_VALUE (x)));
  } else {
    SCM_WTA_DISPATCH_1 (g_abs, x, 1, s_abs);
  }
}


SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient);
/* "Return the quotient of the numbers @var{x} and @var{y}."
 */
SCM
scm_quotient (SCM x, SCM y)
{
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_quotient);
      } else {
        long z = xx / yy;
        if (SCM_FIXABLE (z)) {
          return SCM_MAKINUM (z);
        } else {
#ifdef SCM_BIGDIG
          return scm_i_long2big (z);
#else
          scm_num_overflow (s_quotient);
#endif
        }
      }
    } else if (SCM_BIGP (y)) {
      if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM
          && scm_bigcomp (abs_most_negative_fixnum, y) == 0)
        {
          /* Special case:  x == fixnum-min && y == abs (fixnum-min) */
          return SCM_MAKINUM (-1);
        }
      else
        return SCM_MAKINUM (0);
    } else {
      SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_quotient);
      } else if (yy == 1) {
        return x;
      } else {
        long z = yy < 0 ? -yy : yy;
        
        if (z < SCM_BIGRAD) {
          SCM sw = scm_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0));
          scm_divbigdig (SCM_BDIGITS (sw), SCM_NUMDIGS (sw), (SCM_BIGDIG) z);
          return scm_i_normbig (sw);
        } else {
#ifndef SCM_DIGSTOOBIG
          long w = scm_pseudolong (z);
          return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                                (SCM_BIGDIG *) & w, SCM_DIGSPERLONG,
                                SCM_BIGSIGN (x) ? (yy > 0) : (yy < 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) ? (yy > 0) : (yy < 0), 2);
#endif
        }
      }
    } else if (SCM_BIGP (y)) {
      return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                            SCM_BDIGITS (y), SCM_NUMDIGS (y),
                            SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 2);
    } else {
      SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient);
  }
}


SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder);
/* "Return the remainder of the numbers @var{x} and @var{y}.\n"
 * "@lisp\n"
 * "(remainder 13 4) @result{} 1\n"
 * "(remainder -13 4) @result{} -1\n"
 * "@end lisp"
 */
SCM
scm_remainder (SCM x, SCM y)
{
  if (SCM_INUMP (x)) {
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_remainder);
      } else {
        long z = SCM_INUM (x) % yy;
        return SCM_MAKINUM (z);
      }
    } else if (SCM_BIGP (y)) {
      if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM
          && scm_bigcomp (abs_most_negative_fixnum, y) == 0)
        {
          /* Special case:  x == fixnum-min && y == abs (fixnum-min) */
          return SCM_MAKINUM (0);
        }
      else
        return x;
    } else {
      SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_remainder);
      } else {
        return scm_divbigint (x, yy, SCM_BIGSIGN (x), 0);
      }
    } else if (SCM_BIGP (y)) {
      return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                            SCM_BDIGITS (y), SCM_NUMDIGS (y),
                            SCM_BIGSIGN (x), 0);
    } else {
      SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder);
  }
}


SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo);
/* "Return the modulo of the numbers @var{x} and @var{y}.\n"
 * "@lisp\n"
 * "(modulo 13 4) @result{} 1\n"
 * "(modulo -13 4) @result{} 3\n"
 * "@end lisp"
 */
SCM
scm_modulo (SCM x, SCM y)
{
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_modulo);
      } else {
        long z = xx % yy;
        return SCM_MAKINUM (((yy < 0) ? (z > 0) : (z < 0)) ? z + yy : z);
      }
    } else if (SCM_BIGP (y)) {
      return (SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)) ? scm_sum (x, y) : x;
    } else {
      SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_modulo);
      } else {
        return scm_divbigint (x, yy, yy < 0,
                              (SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)) ? 1 : 0);
      }
    } else if (SCM_BIGP (y)) {
      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);
    } else {
      SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo);
  }
}


SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd);
/* "Return the greatest common divisor of all arguments.\n"
 * "If called without arguments, 0 is returned."
 */
SCM
scm_gcd (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      return SCM_INUM0;
    } else {
      return x;
    }
  }

 tailrec:
  if (SCM_INUMP (x)) {
    if (SCM_INUMP (y)) {
      long xx = SCM_INUM (x);
      long yy = SCM_INUM (y);
      long u = xx < 0 ? -xx : xx;
      long v = yy < 0 ? -yy : yy;
      long result;

      if (xx == 0) {
        result = v;
      } else if (yy == 0) {
        result = u;
      } else {
        long k = 1;
        long t;

        /* Determine a common factor 2^k */
        while (!(1 & (u | v))) {
          k <<= 1;
          u >>= 1;
          v >>= 1;
        }

        /* Now, any factor 2^n can be eliminated */
        if (u & 1) {
          t = -v;
        } else {
          t = u;
        b3:
          t = SCM_SRS (t, 1);
        }
        if (!(1 & t))
          goto b3;
        if (t > 0)
          u = t;
        else
          v = -t;
        t = u - v;
        if (t != 0)
          goto b3;

        result = u * k;
      }
      if (SCM_POSFIXABLE (result)) {
        return SCM_MAKINUM (result);
      } else {
#ifdef SCM_BIGDIG
        return scm_i_long2big (result);
#else
        scm_num_overflow (s_gcd);
#endif
      }
    } else if (SCM_BIGP (y)) {
      SCM_SWAP (x, y);
      goto big_gcd;
    } else {
      SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd);
    }
  } else if (SCM_BIGP (x)) {
  big_gcd:
    if (SCM_BIGSIGN (x))
      x = scm_i_copybig (x, 0);
  newy:
    if (SCM_INUMP (y)) {
      if (SCM_EQ_P (y, SCM_INUM0)) {
        return x;
      } else {
        goto swaprec;
      }
    } else if (SCM_BIGP (y)) {
      if (SCM_BIGSIGN (y))
        y = scm_i_copybig (y, 0);
      switch (scm_bigcomp (x, y))
        {
        case -1:  /* x > y */
        swaprec:
        {
          SCM t = scm_remainder (x, y);
          x = y;
          y = t;
        }
        goto tailrec;
        case 1:  /* x < y */
          y = scm_remainder (y, x);
          goto newy;
        default:  /* x == y */
          return x;
        }
      /* instead of the switch, we could just
         return scm_gcd (y, scm_modulo (x, y)); */
    } else {
      SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd);
  }
}


SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm);
/* "Return the least common multiple of the arguments.\n"
 * "If called without arguments, 1 is returned."
 */
SCM
scm_lcm (SCM n1, SCM n2)
{
  if (SCM_UNBNDP (n2)) {
    if (SCM_UNBNDP (n1)) {
      return SCM_MAKINUM (1L);
    } else {
      n2 = SCM_MAKINUM (1L);
    }
  };

#ifndef SCM_BIGDIG
  SCM_GASSERT2 (SCM_INUMP (n1), g_lcm, n1, n2, SCM_ARG1, s_lcm);
  SCM_GASSERT2 (SCM_INUMP (n2), g_lcm, n1, n2, SCM_ARGn, s_lcm);
#else
  SCM_GASSERT2 (SCM_INUMP (n1) || SCM_BIGP (n1),
                g_lcm, n1, n2, SCM_ARG1, s_lcm);
  SCM_GASSERT2 (SCM_INUMP (n2) || SCM_BIGP (n2),
                g_lcm, n1, n2, SCM_ARGn, s_lcm);
#endif

  {
    SCM d = scm_gcd (n1, n2);
    if (SCM_EQ_P (d, SCM_INUM0)) {
      return d;
    } else {
      return scm_abs (scm_product (n1, scm_quotient (n2, d)));
    }
  }
}


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


/* Emulating 2's complement bignums with sign magnitude arithmetic:

   Logand:
   X    Y       Result  Method:
                 (len)
   +    +       + x     (map digit:logand X Y)
   +    -       + x     (map digit:logand X (lognot (+ -1 Y)))
   -    +       + y     (map digit:logand (lognot (+ -1 X)) Y)
   -    -       -       (+ 1 (map digit:logior (+ -1 X) (+ -1 Y)))

   Logior:
   X    Y       Result  Method:

   +    +       +       (map digit:logior X Y)
   +    -       - y     (+ 1 (map digit:logand (lognot X) (+ -1 Y)))
   -    +       - x     (+ 1 (map digit:logand (+ -1 X) (lognot Y)))
   -    -       - x     (+ 1 (map digit:logand (+ -1 X) (+ -1 Y)))

   Logxor:
   X    Y       Result  Method:

   +    +       +       (map digit:logxor X Y)
   +    -       -       (+ 1 (map digit:logxor X (+ -1 Y)))
   -    +       -       (+ 1 (map digit:logxor (+ -1 X) Y))
   -    -       +       (map digit:logxor (+ -1 X) (+ -1 Y))

   Logtest:
   X    Y       Result

   +    +       (any digit:logand X Y)
   +    -       (any digit:logand X (lognot (+ -1 Y)))
   -    +       (any digit:logand (lognot (+ -1 X)) Y)
   -    -       #t

*/

#ifdef SCM_BIGDIG

SCM scm_copy_big_dec(SCM b, int sign);
SCM scm_copy_smaller(SCM_BIGDIG *x, size_t nx, int zsgn);
SCM scm_big_ior(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy);
SCM scm_big_xor(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy);
SCM scm_big_and(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int zsgn);
SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy);

SCM scm_copy_big_dec(SCM b, int sign)
{
  long num = -1;
  size_t nx = SCM_NUMDIGS(b);
  size_t i = 0;
  SCM ans = scm_i_mkbig(nx, sign);
  SCM_BIGDIG *src = SCM_BDIGITS(b), *dst = SCM_BDIGITS(ans);
  if SCM_BIGSIGN(b) do {
    num += src[i];
    if (num < 0) {dst[i] = num + SCM_BIGRAD; num = -1;}
    else {dst[i] = SCM_BIGLO(num); num = 0;}
  } while (++i < nx);
  else
    while (nx--) dst[nx] = src[nx];
  return ans;
}

SCM scm_copy_smaller(SCM_BIGDIG *x, size_t nx, int zsgn)
{
  long num = -1;
  size_t i = 0;
  SCM z = scm_i_mkbig(nx, zsgn);
  SCM_BIGDIG *zds = SCM_BDIGITS(z);
  if (zsgn) do {
    num += x[i];
    if (num < 0) {zds[i] = num + SCM_BIGRAD; num = -1;}
    else {zds[i] = SCM_BIGLO(num); num = 0;}
  } while (++i < nx);
  else do zds[i] = x[i]; while (++i < nx);
  return z;
}

SCM scm_big_ior(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy)
/* Assumes nx <= SCM_NUMDIGS(bigy) */
/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */
{
  long num = -1;
  size_t i = 0, ny = SCM_NUMDIGS(bigy);
  SCM z = scm_copy_big_dec (bigy, xsgn & SCM_BIGSIGN (bigy));
  SCM_BIGDIG *zds = SCM_BDIGITS(z);
  if (xsgn) {
    do {
      num += x[i];
      if (num < 0) {zds[i] |= num + SCM_BIGRAD; num = -1;}
      else {zds[i] |= SCM_BIGLO(num); num = 0;}
    } while (++i < nx);
    /* =========  Need to increment zds now =========== */
    i = 0; num = 1;
    while (i < ny) {
      num += zds[i];
      zds[i++] = SCM_BIGLO(num);
      num = SCM_BIGDN(num);
      if (!num) return z;
    }
    scm_i_adjbig(z, 1 + ny);            /* OOPS, overflowed into next digit. */
    SCM_BDIGITS(z)[ny] = 1;
    return z;
  }
  else do zds[i] = zds[i] | x[i]; while (++i < nx);
  return z;
}

SCM scm_big_xor(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy)
/* Assumes nx <= SCM_NUMDIGS(bigy) */
/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */
{
  long num = -1;
  size_t i = 0, ny = SCM_NUMDIGS(bigy);
  SCM z = scm_copy_big_dec(bigy, xsgn ^ SCM_BIGSIGN(bigy));
  SCM_BIGDIG *zds = SCM_BDIGITS(z);
  if (xsgn) do {
    num += x[i];
    if (num < 0) {zds[i] ^= num + SCM_BIGRAD; num = -1;}
    else {zds[i] ^= SCM_BIGLO(num); num = 0;}
  } while (++i < nx);
  else do {
    zds[i] = zds[i] ^ x[i];
  } while (++i < nx);

  if (xsgn ^ SCM_BIGSIGN(bigy)) {
    /* =========  Need to increment zds now =========== */
    i = 0; num = 1;
    while (i < ny) {
      num += zds[i];
      zds[i++] = SCM_BIGLO(num);
      num = SCM_BIGDN(num);
      if (!num) return scm_i_normbig(z);
    }
  }
  return scm_i_normbig(z);
}

SCM scm_big_and(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int zsgn)
/* Assumes nx <= SCM_NUMDIGS(bigy) */
/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */
/* return sign equals either 0 or SCM_BIGSIGNFLAG */
{
  long num = -1;
  size_t i = 0;
  SCM z;
  SCM_BIGDIG *zds;
  if (xsgn==zsgn) {
    z = scm_copy_smaller(x, nx, zsgn);
    x = SCM_BDIGITS(bigy);
    xsgn = SCM_BIGSIGN(bigy);
  }
  else z = scm_copy_big_dec(bigy, zsgn);
  zds = SCM_BDIGITS(z);

  if (zsgn) {
    if (xsgn) do {
      num += x[i];
      if (num < 0) {zds[i] &= num + SCM_BIGRAD; num = -1;}
      else {zds[i] &= SCM_BIGLO(num); num = 0;}
    } while (++i < nx);
    else do zds[i] = zds[i] & ~x[i]; while (++i < nx);
    /* =========  need to increment zds now =========== */
    i = 0; num = 1;
    while (i < nx) {
      num += zds[i];
      zds[i++] = SCM_BIGLO(num);
      num = SCM_BIGDN(num);
      if (!num) return scm_i_normbig(z);
    }
  }
  else if (xsgn) {
    unsigned long int carry = 1;
    do {
      unsigned long int mask = (SCM_BIGDIG) ~x[i] + carry;
      zds[i] = zds[i] & (SCM_BIGDIG) mask;
      carry = (mask >= SCM_BIGRAD) ? 1 : 0;
    } while (++i < nx);
  } else do zds[i] = zds[i] & x[i]; while (++i < nx);
  return scm_i_normbig(z);
}

SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy)
/* Assumes nx <= SCM_NUMDIGS(bigy) */
/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */
{
  SCM_BIGDIG *y;
  size_t i = 0;
  long num = -1;
  if (SCM_BIGSIGN(bigy) & xsgn) return SCM_BOOL_T;
  if (SCM_NUMDIGS(bigy) != nx && xsgn) return SCM_BOOL_T;
  y = SCM_BDIGITS(bigy);
  if (xsgn)
    do {
      num += x[i];
      if (num < 0) {
        if (y[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T;
        num = -1;
      }
      else {
        if (y[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T;
        num = 0;
      }
    } while (++i < nx);
  else if SCM_BIGSIGN(bigy)
    do {
      num += y[i];
      if (num < 0) {
        if (x[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T;
        num = -1;
      }
      else {
        if (x[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T;
        num = 0;
      }
    } while (++i < nx);
  else
    do if (x[i] & y[i]) return SCM_BOOL_T;
    while (++i < nx);
  return SCM_BOOL_F;
}

#endif

SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr,
             (SCM n1, SCM n2),
             "Return the bitwise AND of the integer arguments.\n\n"
             "@lisp\n"
             "(logand) @result{} -1\n"
             "(logand 7) @result{} 7\n"
             "(logand #b111 #b011 #\b001) @result{} 1\n"
             "@end lisp")
#define FUNC_NAME s_scm_logand
{
  long int nn1;

  if (SCM_UNBNDP (n2)) {
    if (SCM_UNBNDP (n1)) {
      return SCM_MAKINUM (-1);
    } else if (!SCM_NUMBERP (n1)) {
      SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
#ifndef SCM_RECKLESS
    } else if (SCM_NUMBERP (n1)) {
      return n1;
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
#else
    } else {
      return n1;
#endif
    }
  }

  if (SCM_INUMP (n1)) {
    nn1 = SCM_INUM (n1);
    if (SCM_INUMP (n2)) {
      long nn2 = SCM_INUM (n2);
      return SCM_MAKINUM (nn1 & nn2);
    } else if SCM_BIGP (n2) {
    intbig: 
      {
# ifndef SCM_DIGSTOOBIG
        long z = scm_pseudolong (nn1);
        if ((nn1 < 0) && SCM_BIGSIGN (n2)) {
          return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, 
                              SCM_BIGSIGNFLAG, n2);
        } else {
          return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0);
        }
# else
        SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
        scm_longdigs (nn1, zdigs);
        if ((nn1 < 0) && SCM_BIGSIGN (n2)) {
          return scm_big_ior (zdigs, SCM_DIGSPERLONG, SCM_BIGSIGNFLAG, n2);
        } else {
          return scm_big_and (zdigs, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0);
        }
# endif
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else if (SCM_BIGP (n1)) {
    if (SCM_INUMP (n2)) {
      SCM_SWAP (n1, n2);
      nn1 = SCM_INUM (n1);
      goto intbig;
    } else if (SCM_BIGP (n2)) {
      if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) {
        SCM_SWAP (n1, n2);
      };
      if ((SCM_BIGSIGN (n1)) && SCM_BIGSIGN (n2)) {
        return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1),
                            SCM_BIGSIGNFLAG, n2);
      } else {
        return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1),
                            SCM_BIGSIGN (n1), n2, 0);
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
  }
}
#undef FUNC_NAME


SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr,
             (SCM n1, SCM n2),
             "Return the bitwise OR of the integer arguments.\n\n"
             "@lisp\n"
             "(logior) @result{} 0\n"
             "(logior 7) @result{} 7\n"
             "(logior #b000 #b001 #b011) @result{} 3\n"
            "@end lisp")
#define FUNC_NAME s_scm_logior
{
  long int nn1;

  if (SCM_UNBNDP (n2)) {
    if (SCM_UNBNDP (n1)) {
      return SCM_INUM0;
#ifndef SCM_RECKLESS
    } else if (SCM_NUMBERP (n1)) {
      return n1;
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
#else
    } else {
      return n1;
#endif
    }
  }

  if (SCM_INUMP (n1)) {
    nn1 = SCM_INUM (n1);
    if (SCM_INUMP (n2)) {
      long nn2 = SCM_INUM (n2);
      return SCM_MAKINUM (nn1 | nn2);
    } else if (SCM_BIGP (n2)) {
    intbig:
      {
# ifndef SCM_DIGSTOOBIG
        long z = scm_pseudolong (nn1);
        if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) {
          return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2);
        } else {
          return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG);
        }
# else
        SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
        scm_longdigs (nn1, zdigs);
        if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) {
          return scm_big_ior (zdigs, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2);
        } else {
          return scm_big_and (zdigs, SCM_DIGSPERLONG, 
                              (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG);
        }
# endif
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else if (SCM_BIGP (n1)) {
    if (SCM_INUMP (n2)) {
      SCM_SWAP (n1, n2); 
      nn1 = SCM_INUM (n1);
      goto intbig;
    } else if (SCM_BIGP (n2)) {
      if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) {
        SCM_SWAP (n1, n2);
      };
      if ((!SCM_BIGSIGN (n1)) && !SCM_BIGSIGN (n2)) {
        return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), 
                            SCM_BIGSIGN (n1), n2);
      } else {
        return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), 
                            SCM_BIGSIGN (n1), n2, SCM_BIGSIGNFLAG);
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
  }
}
#undef FUNC_NAME


SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr,
             (SCM n1, SCM n2),
             "Return the bitwise XOR of the integer arguments.  A bit is\n"
             "set in the result if it is set in an odd number of arguments.\n"
             "@lisp\n"
             "(logxor) @result{} 0\n"
             "(logxor 7) @result{} 7\n"
             "(logxor #b000 #b001 #b011) @result{} 2\n"
             "(logxor #b000 #b001 #b011 #b011) @result{} 1\n"
            "@end lisp")
#define FUNC_NAME s_scm_logxor
{
  long int nn1;

  if (SCM_UNBNDP (n2)) {
    if (SCM_UNBNDP (n1)) {
      return SCM_INUM0;
#ifndef SCM_RECKLESS
    } else if (SCM_NUMBERP (n1)) {
      return n1;
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
#else
    } else {
      return n1;
#endif
    }
  }

  if (SCM_INUMP (n1)) {
    nn1 = SCM_INUM (n1);
    if (SCM_INUMP (n2)) {
      long nn2 = SCM_INUM (n2);
      return SCM_MAKINUM (nn1 ^ nn2);
    } else if (SCM_BIGP (n2)) {
    intbig: 
      {
# ifndef SCM_DIGSTOOBIG
        long z = scm_pseudolong (nn1);
        return scm_big_xor ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, 
                            (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2);
# else
        SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
        scm_longdigs (nn1, zdigs);
        return scm_big_xor (zdigs, SCM_DIGSPERLONG, 
                            (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2);
# endif
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else if (SCM_BIGP (n1)) {
    if (SCM_INUMP (n2)) {
      SCM_SWAP (n1, n2);
      nn1 = SCM_INUM (n1);
      goto intbig;
    } else if (SCM_BIGP (n2)) {
      if (SCM_NUMDIGS(n1) > SCM_NUMDIGS(n2)) {
        SCM_SWAP (n1, n2);
      }
      return scm_big_xor (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), 
                          SCM_BIGSIGN (n1), n2);
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
  }
}
#undef FUNC_NAME


SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0,
            (SCM j, SCM k),
            "@lisp\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 lisp")
#define FUNC_NAME s_scm_logtest
{
  long int nj;

  if (SCM_INUMP (j)) {
    nj = SCM_INUM (j);
    if (SCM_INUMP (k)) {
      long nk = SCM_INUM (k);
      return SCM_BOOL (nj & nk);
    } else if (SCM_BIGP (k)) {
    intbig: 
      {
# ifndef SCM_DIGSTOOBIG
        long z = scm_pseudolong (nj);
        return scm_big_test ((SCM_BIGDIG *)&z, SCM_DIGSPERLONG, 
                             (nj < 0) ? SCM_BIGSIGNFLAG : 0, k);
# else
        SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
        scm_longdigs (nj, zdigs);
        return scm_big_test (zdigs, SCM_DIGSPERLONG, 
                             (nj < 0) ? SCM_BIGSIGNFLAG : 0, k);
# endif
      }
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
    }
  } else if (SCM_BIGP (j)) {
    if (SCM_INUMP (k)) {
      SCM_SWAP (j, k);
      nj = SCM_INUM (j);
      goto intbig;
    } else if (SCM_BIGP (k)) {
      if (SCM_NUMDIGS (j) > SCM_NUMDIGS (k)) {
        SCM_SWAP (j, k);
      }
      return scm_big_test (SCM_BDIGITS (j), SCM_NUMDIGS (j), 
                           SCM_BIGSIGN (j), k);
    } else {
      SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, j);
  }
}
#undef FUNC_NAME


SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0,
            (SCM index, SCM j),
            "@lisp\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 lisp")
#define FUNC_NAME s_scm_logbit_p
{
  unsigned long int iindex;

  SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0);
  iindex = (unsigned long int) SCM_INUM (index);

  if (SCM_INUMP (j)) {
    return SCM_BOOL ((1L << iindex) & SCM_INUM (j));
  } else if (SCM_BIGP (j)) {
    if (SCM_NUMDIGS (j) * SCM_BITSPERDIG < iindex) {
      return SCM_BOOL_F;
    } else if (SCM_BIGSIGN (j)) {
      long num = -1;
      size_t i = 0;
      SCM_BIGDIG * x = SCM_BDIGITS (j);
      size_t nx = iindex / SCM_BITSPERDIG;
      while (1) {
        num += x[i];
        if (nx == i++) {
          return SCM_BOOL (((1L << (iindex % SCM_BITSPERDIG)) & num) == 0);
        } else if (num < 0) {
          num = -1;
        } else {
          num = 0;
        }
      }
    } else {
      return SCM_BOOL (SCM_BDIGITS (j) [iindex / SCM_BITSPERDIG]
                       & (1L << (iindex % SCM_BITSPERDIG)));
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG2, j);
  }
}
#undef FUNC_NAME


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

SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0,
            (SCM n, SCM k),
            "Return @var{n} raised to the non-negative integer exponent\n"
            "@var{k}.\n"
            "\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_EQ_P (n, SCM_INUM0) || SCM_EQ_P (n, acc))
    return n;
  else if (SCM_EQ_P (n, SCM_MAKINUM (-1L)))
    return SCM_FALSEP (scm_even_p (k)) ? n : acc;
#endif
  if (SCM_REALP (k))
    {
      double r = SCM_REAL_VALUE (k);
      i2 = r;
      if (i2 != r)
        SCM_WRONG_TYPE_ARG (2, k);
    }
  else
    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),
            "The function ash performs an arithmetic shift left by @var{cnt}\n"
            "bits (or shift right, if @var{cnt} is negative).  'Arithmetic'\n"
            "means, that the function does not guarantee to keep the bit\n"
            "structure of @var{n}, but rather guarantees that the result\n"
            "will always be rounded towards minus infinity.  Therefore, the\n"
            "results of ash and a corresponding bitwise shift will differ if\n"
            "@var{n} is negative.\n"
            "\n"
            "Formally, the function returns an integer equivalent to\n"
            "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n"
            "\n"
            "@lisp\n"
            "(number->string (ash #b1 3) 2)     @result{} \"1000\"\n"
            "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n"
            "@end lisp")
#define FUNC_NAME s_scm_ash
{
  long bits_to_shift;

#ifndef SCM_BIGDIG
  SCM_VALIDATE_INUM (1, n)
#endif
  SCM_VALIDATE_INUM (2, cnt);

  bits_to_shift = SCM_INUM (cnt);
#ifdef SCM_BIGDIG
  if (bits_to_shift < 0) {
    /* Shift right by abs(cnt) bits.  This is realized as a division by
       div:=2^abs(cnt).  However, to guarantee the floor rounding, negative
       values require some special treatment.
     */
    SCM div = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-bits_to_shift));
    if (SCM_FALSEP (scm_negative_p (n)))
      return scm_quotient (n, div);
    else
      return scm_sum (SCM_MAKINUM (-1L),
                      scm_quotient (scm_sum (SCM_MAKINUM (1L), n), div));
  } else
    /* Shift left is done by multiplication with 2^CNT */
    return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt));
#else
  if (bits_to_shift < 0)
    /* Signed right shift (SCM_SRS does it right) by abs(cnt) bits. */
    return SCM_MAKINUM (SCM_SRS (SCM_INUM (n), -bits_to_shift));
  else {
    /* Shift left, but make sure not to leave the range of inums */
    SCM res = SCM_MAKINUM (SCM_INUM (n) << cnt);
    if (SCM_INUM (res) >> cnt != SCM_INUM (n))
      scm_num_overflow (FUNC_NAME);
    return res;
  }
#endif
}
#undef FUNC_NAME


SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0,
            (SCM n, SCM start, SCM end),
            "Return the integer composed of the @var{start} (inclusive)\n"
            "through @var{end} (exclusive) bits of @var{n}.  The\n"
            "@var{start}th bit becomes the 0-th bit in the result.\n"
            "\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
{
  unsigned long int istart, iend;
  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));

  if (SCM_INUMP (n)) {
    long int in = SCM_INUM (n);
    unsigned long int bits = iend - istart;

    if (in < 0 && bits >= SCM_I_FIXNUM_BIT)
      {
        /* Since we emulate two's complement encoded numbers, this special
         * case requires us to produce a result that has more bits than can be
         * stored in a fixnum.  Thus, we fall back to the more general
         * algorithm that is used for bignums.  
         */
        goto generalcase;
      }

    if (istart < SCM_I_FIXNUM_BIT)
      {
        in = in >> istart;
        if (bits < SCM_I_FIXNUM_BIT)
          return SCM_MAKINUM (in & ((1L << bits) - 1));
        else /* we know: in >= 0 */
          return SCM_MAKINUM (in);
      }
    else if (in < 0)
      {
        return SCM_MAKINUM (-1L & ((1L << bits) - 1));
      }
    else
      {
        return SCM_MAKINUM (0);
      }
  } else if (SCM_BIGP (n)) {
  generalcase:
    {
      SCM num1 = SCM_MAKINUM (1L);
      SCM num2 = SCM_MAKINUM (2L);
      SCM bits = SCM_MAKINUM (iend - istart);
      SCM mask  = scm_difference (scm_integer_expt (num2, bits), num1);
      return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart)));
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
  }
}
#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),
            "Return the number of bits in integer @var{n}.  If integer is\n"
            "positive, the 1-bits in its binary representation are counted.\n"
            "If negative, the 0-bits in its two's-complement binary\n"
            "representation are counted.  If 0, 0 is returned.\n"
            "\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
{
  if (SCM_INUMP (n)) {
    unsigned long int c = 0;
    long int nn = SCM_INUM (n);
    if (nn < 0) {
      nn = -1 - nn;
    };
    while (nn) {
      c += scm_logtab[15 & nn];
      nn >>= 4;
    };
    return SCM_MAKINUM (c);
  } else if (SCM_BIGP (n)) {
    if (SCM_BIGSIGN (n)) {
      return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n));
    } else {
      unsigned long int c = 0;
      size_t i = SCM_NUMDIGS (n);
      SCM_BIGDIG * ds = SCM_BDIGITS (n);
      while (i--) {
        SCM_BIGDIG d;
        for (d = ds[i]; d; d >>= 4) {
          c += scm_logtab[15 & d];
        }
      }
      return SCM_MAKINUM (c);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
  }
}
#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),
            "Return the number of bits necessary to represent @var{n}.\n"
            "\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
{
  if (SCM_INUMP (n)) {
    unsigned long int c = 0;
    unsigned int l = 4;
    long int nn = SCM_INUM (n);
    if (nn < 0) {
      nn = -1 - nn;
    };
    while (nn) {
      c += 4;
      l = scm_ilentab [15 & nn];
      nn >>= 4;
    };
    return SCM_MAKINUM (c - 4 + l);
  } else if (SCM_BIGP (n)) {
    if (SCM_BIGSIGN (n)) {
      return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n));
    } else {
      unsigned long int digs = SCM_NUMDIGS (n) - 1;
      unsigned long int c = digs * SCM_BITSPERDIG;
      unsigned int l = 4;
      SCM_BIGDIG * ds = SCM_BDIGITS (n);
      SCM_BIGDIG d = ds [digs];
      while (d) {
        c += 4;
        l = scm_ilentab [15 & d];
        d >>= 4;
      };
      return SCM_MAKINUM (c - 4 + l);
    }
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
  }
}
#undef FUNC_NAME


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

SCM
scm_i_mkbig (size_t nlen, int sign)
{
  SCM v;
  SCM_BIGDIG *base;

  if (((nlen << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen)
    scm_memory_error (s_bignum);

  base = scm_gc_malloc (nlen * sizeof (SCM_BIGDIG), s_bignum);

  v = scm_cell (SCM_MAKE_BIGNUM_TAG (nlen, sign), (scm_t_bits) base);
  return v;
}

SCM
scm_i_big2inum (SCM b, size_t l)
{
  unsigned long num = 0;
  SCM_BIGDIG *tmp = SCM_BDIGITS (b);
  while (l--)
    num = SCM_BIGUP (num) + tmp[l];
  if (!SCM_BIGSIGN (b))
    {
      if (SCM_POSFIXABLE (num))
        return SCM_MAKINUM (num);
    }
  else if (num <= -SCM_MOST_NEGATIVE_FIXNUM)
    return SCM_MAKINUM (-num);
  return b;
}

static const char s_adjbig[] = "scm_i_adjbig";

SCM
scm_i_adjbig (SCM b, size_t nlen)
{
  size_t nsiz = nlen;
  if (((nsiz << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen)
    scm_memory_error (s_adjbig);

  SCM_DEFER_INTS;
  {
    SCM_BIGDIG *digits
      = ((SCM_BIGDIG *)
         scm_gc_realloc (SCM_BDIGITS (b),
                         SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG),
                         nsiz * sizeof (SCM_BIGDIG), s_bignum));

    SCM_SET_BIGNUM_BASE (b, digits);
    SCM_SETNUMDIGS (b, nsiz, SCM_BIGSIGN (b));
  }
  SCM_ALLOW_INTS;
  return b;
}

SCM
scm_i_normbig (SCM b)
{
#ifndef _UNICOS
  size_t 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_i_big2inum (b, (size_t) nlen)))
      return b;
  if (SCM_NUMDIGS (b) == nlen)
    return b;
  return scm_i_adjbig (b, (size_t) nlen);
}

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

int
scm_bigcomp (SCM x, SCM y)
{
  int xsign = SCM_BIGSIGN (x);
  int ysign = SCM_BIGSIGN (y);
  size_t 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;
  size_t 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[])
{
  size_t 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, size_t nx, int xsgn, SCM bigy, int sgny)
{
  /* Assumes nx <= SCM_NUMDIGS(bigy) */
  /* Assumes xsgn and sgny scm_equal either 0 or SCM_BIGSIGNFLAG */
  long num = 0;
  size_t i = 0, ny = SCM_NUMDIGS (bigy);
  SCM z = scm_i_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_SET_CELL_WORD_0 (z, SCM_CELL_WORD_0 (z) ^ SCM_BIGSIGNFLAG);
          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_i_adjbig (z, ny + 1);
          SCM_BDIGITS (z)[ny] = num;
          return z;
        }
    }
  return scm_i_normbig (z);
}


SCM
scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn)
{
  size_t i = 0, j = nx + ny;
  unsigned long n = 0;
  SCM z = scm_i_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_i_normbig (z);
}


unsigned int
scm_divbigdig (SCM_BIGDIG * ds, size_t 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;
}



static 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);
      size_t 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
  }
}


static SCM
scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes)
{
  /* modes description
     0  remainder
     1  scm_modulo
     2  quotient
     3  quotient but returns SCM_UNDEFINED if division is not exact. */
  size_t 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_i_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_i_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 SCM_UNDEFINED;   /* the division is not exact */
      }

  z = scm_i_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_i_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 SCM_UNDEFINED;
    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_i_big2inum (z, j)))
      return z;
  return scm_i_adjbig (z, j);
}
#endif
\f




/*** NUMBERS -> STRINGS ***/
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 size_t
idbl2str (double f, char *a)
{
  int efmt, dpt, d, i, wp = scm_dblprec;
  size_t 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 size_t
iflo2str (SCM flt, char *str)
{
  size_t i;
  if (SCM_REALP (flt))
    i = idbl2str (SCM_REAL_VALUE (flt), str);
  else
    {
      i = idbl2str (SCM_COMPLEX_REAL (flt), str);
      if (SCM_COMPLEX_IMAG (flt) != 0.0)
        {
          if (0 <= SCM_COMPLEX_IMAG (flt))
            str[i++] = '+';
          i += idbl2str (SCM_COMPLEX_IMAG (flt), &str[i]);
          str[i++] = 'i';
        }
    }
  return i;
}

/* 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  */
size_t
scm_iint2str (long num, int rad, char *p)
{
  size_t j = 1;
  size_t 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_i_copybig (b, 0); /* sign of temp doesn't matter */
  register SCM_BIGDIG *ds = SCM_BDIGITS (t);
  size_t i = SCM_NUMDIGS (t);
  size_t j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2
    : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2
    : (SCM_BITSPERDIG * i) + 2;
  size_t k = 0;
  size_t radct = 0;
  SCM_BIGDIG radpow = 1, radmod = 0;
  SCM ss = scm_allocate_string (j);
  char *s = SCM_STRING_CHARS (ss), c;
  while ((long) radpow * radix < SCM_BIGRAD)
    {
      radpow *= radix;
      radct++;
    }
  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;
    }

  if (SCM_BIGSIGN (b))
    s[--j] = '-';

  if (j > 0)
    {
      /* The pre-reserved string length was too large. */
      unsigned long int length = SCM_STRING_LENGTH (ss);
      ss = scm_substring (ss, SCM_MAKINUM (j), SCM_MAKINUM (length));
    }

  return scm_return_first (ss, t);
}
#endif


SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0,
            (SCM n, SCM radix),
            "Return a string holding the external representation of the\n"
            "number @var{n} in the given @var{radix}.  If @var{n} is\n"
            "inexact, a radix of 10 will be used.")
#define FUNC_NAME s_scm_number_to_string
{
  int base;

  if (SCM_UNBNDP (radix)) {
    base = 10;
  } else {
    SCM_VALIDATE_INUM (2, radix);
    base = SCM_INUM (radix);
    SCM_ASSERT_RANGE (2, radix, base >= 2);
  }

  if (SCM_INUMP (n)) {
    char num_buf [SCM_INTBUFLEN];
    size_t length = scm_iint2str (SCM_INUM (n), base, num_buf);
    return scm_mem2string (num_buf, length);
  } else if (SCM_BIGP (n)) {
    return big2str (n, (unsigned int) base);
  } else if (SCM_INEXACTP (n)) {
    char num_buf [FLOBUFLEN];
    return scm_mem2string (num_buf, iflo2str (n, num_buf));
  } else {
    SCM_WRONG_TYPE_ARG (1, n);
  }
}
#undef FUNC_NAME


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

int
scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
{
  char num_buf[FLOBUFLEN];
  scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port);
  return !0;
}

int
scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
{
  char num_buf[FLOBUFLEN];
  scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port);
  return !0;
}

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


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

/* The following functions implement the conversion from strings to numbers.
 * The implementation somehow follows the grammar for numbers as it is given
 * in R5RS.  Thus, the functions resemble syntactic units (<ureal R>,
 * <uinteger R>, ...) that are used to build up numbers in the grammar.  Some
 * points should be noted about the implementation:
 * * Each function keeps a local index variable 'idx' that points at the
 * current position within the parsed string.  The global index is only
 * updated if the function could parse the corresponding syntactic unit
 * successfully.
 * * Similarly, the functions keep track of indicators of inexactness ('#',
 * '.' or exponents) using local variables ('hash_seen', 'x').  Again, the
 * global exactness information is only updated after each part has been
 * successfully parsed.
 * * Sequences of digits are parsed into temporary variables holding fixnums.
 * Only if these fixnums would overflow, the result variables are updated
 * using the standard functions scm_add, scm_product, scm_divide etc.  Then,
 * the temporary variables holding the fixnums are cleared, and the process
 * starts over again.  If for example fixnums were able to store five decimal
 * digits, a number 1234567890 would be parsed in two parts 12345 and 67890,
 * and the result was computed as 12345 * 100000 + 67890.  In other words,
 * only every five digits two bignum operations were performed.
 */

enum t_exactness {NO_EXACTNESS, INEXACT, EXACT};

/* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */

/* In non ASCII-style encodings the following macro might not work. */
#define XDIGIT2UINT(d) (isdigit (d) ? (d) - '0' : tolower (d) - 'a' + 10)

static SCM
mem2uinteger (const char* mem, size_t len, unsigned int *p_idx,
              unsigned int radix, enum t_exactness *p_exactness)
{
  unsigned int idx = *p_idx;
  unsigned int hash_seen = 0;
  scm_t_bits shift = 1;
  scm_t_bits add = 0;
  unsigned int digit_value;
  SCM result;
  char c;

  if (idx == len)
    return SCM_BOOL_F;

  c = mem[idx];
  if (!isxdigit (c))
    return SCM_BOOL_F;
  digit_value = XDIGIT2UINT (c);
  if (digit_value >= radix)
    return SCM_BOOL_F;

  idx++;
  result = SCM_MAKINUM (digit_value);
  while (idx != len)
    {
      char c = mem[idx];
      if (isxdigit (c))
        {
          if (hash_seen)
            break;
          digit_value = XDIGIT2UINT (c);
          if (digit_value >= radix)
            break;
        }
      else if (c == '#')
        {
          hash_seen = 1;
          digit_value = 0;
        }
      else
        break;

      idx++;
      if (SCM_MOST_POSITIVE_FIXNUM / radix < shift)
        {
          result = scm_product (result, SCM_MAKINUM (shift));
          if (add > 0)
            result = scm_sum (result, SCM_MAKINUM (add));

          shift = radix;
          add = digit_value;
        }
      else
        {
          shift = shift * radix;
          add = add * radix + digit_value;
        }
    };

  if (shift > 1)
    result = scm_product (result, SCM_MAKINUM (shift));
  if (add > 0)
    result = scm_sum (result, SCM_MAKINUM (add));

  *p_idx = idx;
  if (hash_seen)
    *p_exactness = INEXACT;

  return result;
}


/* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>.  Only
 * covers the parts of the rules that start at a potential point.  The value
 * of the digits up to the point have been parsed by the caller and are given
 * in variable result.  The content of *p_exactness indicates, whether a hash
 * has already been seen in the digits before the point.
 */

/* In non ASCII-style encodings the following macro might not work. */
#define DIGIT2UINT(d) ((d) - '0')

static SCM
mem2decimal_from_point (SCM result, const char* mem, size_t len, 
                        unsigned int *p_idx, enum t_exactness *p_exactness)
{
  unsigned int idx = *p_idx;
  enum t_exactness x = *p_exactness;

  if (idx == len)
    return result;

  if (mem[idx] == '.')
    {
      scm_t_bits shift = 1;
      scm_t_bits add = 0;
      unsigned int digit_value;
      SCM big_shift = SCM_MAKINUM (1);

      idx++;
      while (idx != len)
        {
          char c = mem[idx];
          if (isdigit (c))
            {
              if (x == INEXACT)
                return SCM_BOOL_F;
              else
                digit_value = DIGIT2UINT (c);
            }
          else if (c == '#')
            {
              x = INEXACT;
              digit_value = 0;
            }
          else
            break;

          idx++;
          if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift)
            {
              big_shift = scm_product (big_shift, SCM_MAKINUM (shift));
              result = scm_product (result, SCM_MAKINUM (shift));
              if (add > 0)
                result = scm_sum (result, SCM_MAKINUM (add));
              
              shift = 10;
              add = digit_value;
            }
          else
            {
              shift = shift * 10;
              add = add * 10 + digit_value;
            }
        };

      if (add > 0)
        {
          big_shift = scm_product (big_shift, SCM_MAKINUM (shift));
          result = scm_product (result, SCM_MAKINUM (shift));
          result = scm_sum (result, SCM_MAKINUM (add));
        }

      result = scm_divide (result, big_shift);

      /* We've seen a decimal point, thus the value is implicitly inexact. */
      x = INEXACT;
    }

  if (idx != len)
    {
      int sign = 1;
      unsigned int start;
      char c;
      int exponent;
      SCM e;

      /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */

      switch (mem[idx])
        {
        case 'd': case 'D':
        case 'e': case 'E':
        case 'f': case 'F':
        case 'l': case 'L':
        case 's': case 'S':
          idx++;
          start = idx;
          c = mem[idx];
          if (c == '-')
            {
              idx++;
              sign = -1;
              c = mem[idx];
            }
          else if (c == '+')
            {
              idx++;
              sign = 1;
              c = mem[idx];
            }
          else
            sign = 1;

          if (!isdigit (c))
            return SCM_BOOL_F;

          idx++;
          exponent = DIGIT2UINT (c);
          while (idx != len)
            {
              char c = mem[idx];
              if (isdigit (c))
                {
                  idx++;
                  if (exponent <= SCM_MAXEXP)
                    exponent = exponent * 10 + DIGIT2UINT (c);
                }
              else
                break;
            }

          if (exponent > SCM_MAXEXP)
            {
              size_t exp_len = idx - start;
              SCM exp_string = scm_mem2string (&mem[start], exp_len);
              SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED);
              scm_out_of_range ("string->number", exp_num);
            }

          e = scm_integer_expt (SCM_MAKINUM (10), SCM_MAKINUM (exponent));
          if (sign == 1)
            result = scm_product (result, e);
          else
            result = scm_divide (result, e);

          /* We've seen an exponent, thus the value is implicitly inexact. */
          x = INEXACT;

          break;

        default:
          break;
        }
    }

  *p_idx = idx;
  if (x == INEXACT)
    *p_exactness = x;

  return result;
}


/* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */

static SCM
mem2ureal (const char* mem, size_t len, unsigned int *p_idx,
           unsigned int radix, enum t_exactness *p_exactness)
{
  unsigned int idx = *p_idx;

  if (idx == len)
    return SCM_BOOL_F;

  if (mem[idx] == '.')
    {
      if (radix != 10)
        return SCM_BOOL_F;
      else if (idx + 1 == len)
        return SCM_BOOL_F;
      else if (!isdigit (mem[idx + 1]))
        return SCM_BOOL_F;
      else
        return mem2decimal_from_point (SCM_MAKINUM (0), mem, len,
                                       p_idx, p_exactness);
    }
  else
    {
      enum t_exactness x = EXACT;
      SCM uinteger;
      SCM result;

      uinteger = mem2uinteger (mem, len, &idx, radix, &x);
      if (SCM_FALSEP (uinteger))
        return SCM_BOOL_F;

      if (idx == len)
        result = uinteger;
      else if (mem[idx] == '/')
        {
          SCM divisor;

          idx++;

          divisor = mem2uinteger (mem, len, &idx, radix, &x);
          if (SCM_FALSEP (divisor))
            return SCM_BOOL_F;

          result = scm_divide (uinteger, divisor);
        }
      else if (radix == 10)
        {
          result = mem2decimal_from_point (uinteger, mem, len, &idx, &x);
          if (SCM_FALSEP (result))
            return SCM_BOOL_F;
        }
      else
        result = uinteger;

      *p_idx = idx;
      if (x == INEXACT)
        *p_exactness = x;

      return result;
    }
}


/* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */

static SCM
mem2complex (const char* mem, size_t len, unsigned int idx,
             unsigned int radix, enum t_exactness *p_exactness)
{
  char c;
  int sign = 0;
  SCM ureal;

  if (idx == len)
    return SCM_BOOL_F;

  c = mem[idx];
  if (c == '+')
    {
      idx++;
      sign = 1;
    }
  else if (c == '-')
    {
      idx++;
      sign = -1;
    }

  if (idx == len)
    return SCM_BOOL_F;

  ureal = mem2ureal (mem, len, &idx, radix, p_exactness);
  if (SCM_FALSEP (ureal))
    {
      /* input must be either +i or -i */

      if (sign == 0)
        return SCM_BOOL_F;

      if (mem[idx] == 'i' || mem[idx] == 'I')
        {
          idx++;
          if (idx != len)
            return SCM_BOOL_F;
          
          return scm_make_rectangular (SCM_MAKINUM (0), SCM_MAKINUM (sign));
        }
      else
        return SCM_BOOL_F;
    }
  else
    {
      if (sign == -1)
        ureal = scm_difference (ureal, SCM_UNDEFINED);

      if (idx == len)
        return ureal;

      c = mem[idx];
      switch (c)
        {
        case 'i': case 'I':
          /* either +<ureal>i or -<ureal>i */

          idx++;
          if (sign == 0)
            return SCM_BOOL_F;
          if (idx != len)
            return SCM_BOOL_F;
          return scm_make_rectangular (SCM_MAKINUM (0), ureal);

        case '@':
          /* polar input: <real>@<real>. */

          idx++;
          if (idx == len)
            return SCM_BOOL_F;
          else
            {
              int sign;
              SCM angle;
              SCM result;

              c = mem[idx];
              if (c == '+')
                {
                  idx++;
                  sign = 1;
                }
              else if (c == '-')
                {
                  idx++;
                  sign = -1;
                }
              else
                sign = 1;

              angle = mem2ureal (mem, len, &idx, radix, p_exactness);
              if (SCM_FALSEP (angle))
                return SCM_BOOL_F;
              if (idx != len)
                return SCM_BOOL_F;

              if (sign == -1)
                angle = scm_difference (angle, SCM_UNDEFINED);

              result = scm_make_polar (ureal, angle);
              return result;
            }
        case '+':
        case '-':
          /* expecting input matching <real>[+-]<ureal>?i */

          idx++;
          if (idx == len)
            return SCM_BOOL_F;
          else
            {
              int sign = (c == '+') ? 1 : -1;
              SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness);

              if (SCM_FALSEP (imag))
                imag = SCM_MAKINUM (sign);
              else if (sign == -1)
                imag = scm_difference (imag, SCM_UNDEFINED);

              if (idx == len)
                return SCM_BOOL_F;
              if (mem[idx] != 'i' && mem[idx] != 'I')
                return SCM_BOOL_F;

              idx++;
              if (idx != len)
                return SCM_BOOL_F;

              return scm_make_rectangular (ureal, imag);
            }
        default:
          return SCM_BOOL_F;
        }
    }
}


/* R5RS, section 7.1.1, lexical structure of numbers: <number> */

enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16};

SCM
scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix)
{
  unsigned int idx = 0;
  unsigned int radix = NO_RADIX;
  enum t_exactness forced_x = NO_EXACTNESS;
  enum t_exactness implicit_x = EXACT;
  SCM result;

  /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */
  while (idx + 2 < len && mem[idx] == '#')
    {
      switch (mem[idx + 1])
        {
        case 'b': case 'B':
          if (radix != NO_RADIX)
            return SCM_BOOL_F;
          radix = DUAL;
          break;
        case 'd': case 'D':
          if (radix != NO_RADIX)
            return SCM_BOOL_F;
          radix = DEC;
          break;
        case 'i': case 'I':
          if (forced_x != NO_EXACTNESS)
            return SCM_BOOL_F;
          forced_x = INEXACT;
          break;
        case 'e': case 'E':
          if (forced_x != NO_EXACTNESS)
            return SCM_BOOL_F;
          forced_x = EXACT;
          break;
        case 'o': case 'O':
          if (radix != NO_RADIX)
            return SCM_BOOL_F;
          radix = OCT;
          break;
        case 'x': case 'X':
          if (radix != NO_RADIX)
            return SCM_BOOL_F;
          radix = HEX;
          break;
        default:
          return SCM_BOOL_F;
        }
      idx += 2;
    }

  /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */
  if (radix == NO_RADIX)
    result = mem2complex (mem, len, idx, default_radix, &implicit_x);
  else
    result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x);

  if (SCM_FALSEP (result))
    return SCM_BOOL_F;

  switch (forced_x)
    {
    case EXACT:
      if (SCM_INEXACTP (result))
        /* FIXME: This may change the value. */
        return scm_inexact_to_exact (result);
      else
        return result;
    case INEXACT:
      if (SCM_INEXACTP (result))
        return result;
      else
        return scm_exact_to_inexact (result);
    case NO_EXACTNESS:
    default:
      if (implicit_x == INEXACT)
        {
          if (SCM_INEXACTP (result))
            return result;
          else
            return scm_exact_to_inexact (result);
        }
      else
        return result;
    }
}


SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0,
            (SCM string, SCM radix),
            "Return a number of the maximally precise representation\n"
            "expressed by the given @var{string}. @var{radix} must be an\n"
            "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n"
            "is a default radix that may be overridden by an explicit radix\n"
            "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n"
            "supplied, then the default radix is 10. If string is not a\n"
            "syntactically valid notation for a number, then\n"
            "@code{string->number} returns @code{#f}.") 
#define FUNC_NAME s_scm_string_to_number
{
  SCM answer;
  int base;
  SCM_VALIDATE_STRING (1, string);
  SCM_VALIDATE_INUM_MIN_DEF_COPY (2,radix,2,10,base);
  answer = scm_i_mem2number (SCM_STRING_CHARS (string),
                           SCM_STRING_LENGTH (string),
                           base);
  return scm_return_first (answer, string);
}
#undef FUNC_NAME


/*** END strs->nums ***/


SCM
scm_make_real (double x)
{
  SCM z;
  z = scm_double_cell (scm_tc16_real, 0, 0, 0);
  SCM_REAL_VALUE (z) = x;
  return z;
}


SCM
scm_make_complex (double x, double y)
{
  if (y == 0.0) {
    return scm_make_real (x);
  } else {
    SCM z;
    SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (2*sizeof (double),
                                                     "complex"));
    SCM_COMPLEX_REAL (z) = x;
    SCM_COMPLEX_IMAG (z) = y;
    return z;
  }
}


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_real_equalp (SCM x, SCM y)
{
  return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
}

SCM
scm_complex_equalp (SCM x, SCM y)
{
  return SCM_BOOL (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)
                   && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y));
}



SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p);
/* "Return @code{#t} if @var{x} is a number, @code{#f}\n"
 * "else.  Note that the sets of complex, real, rational and\n"
 * "integer values form subsets of the set of numbers, i. e. the\n"
 * "predicate will be fulfilled for any number."
 */
SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, 
            (SCM x),
            "Return @code{#t} if @var{x} is a complex number, @code{#f}\n"
            "otherwise.  Note that the sets of real, rational and integer\n"
            "values form subsets of the set of complex numbers, i. e. the\n"
            "predicate will also be fulfilled if @var{x} is a real,\n"
            "rational or integer number.")
#define FUNC_NAME s_scm_number_p
{
  return SCM_BOOL (SCM_NUMBERP (x));
}
#undef FUNC_NAME


SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p);
/* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n"
 * "Note that the sets of integer and rational values form a subset\n"
 * "of the set of real numbers, i. e. the predicate will also\n"
 * "be fulfilled if @var{x} is an integer or a rational number."
 */
SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0, 
            (SCM x),
            "Return @code{#t} if @var{x} is a rational number, @code{#f}\n"
            "otherwise.  Note that the set of integer values forms a subset of\n"
            "the set of rational numbers, i. e. the predicate will also be\n"
            "fulfilled if @var{x} is an integer number.  Real numbers\n"
            "will also satisfy this predicate, because of their limited\n"
            "precision.")
#define FUNC_NAME s_scm_real_p
{
  if (SCM_INUMP (x)) {
    return SCM_BOOL_T;
  } else if (SCM_IMP (x)) {
    return SCM_BOOL_F;
  } else if (SCM_REALP (x)) {
    return SCM_BOOL_T;
  } else if (SCM_BIGP (x)) {
    return SCM_BOOL_T;
  } else {
    return SCM_BOOL_F;
  }
}
#undef FUNC_NAME


SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, 
            (SCM x),
            "Return @code{#t} if @var{x} is an integer number, @code{#f}\n"
            "else.")
#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;
  if (SCM_BIGP (x))
    return SCM_BOOL_T;
  if (!SCM_INEXACTP (x))
    return SCM_BOOL_F;
  if (SCM_COMPLEXP (x))
    return SCM_BOOL_F;
  r = SCM_REAL_VALUE (x);
  if (r == floor (r))
    return SCM_BOOL_T;
  return SCM_BOOL_F;
}
#undef FUNC_NAME


SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, 
            (SCM x),
            "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n"
            "else.")
#define FUNC_NAME s_scm_inexact_p
{
  return SCM_BOOL (SCM_INEXACTP (x));
}
#undef FUNC_NAME


SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p);
/* "Return @code{#t} if all parameters are numerically equal."  */
SCM
scm_num_eq_p (SCM x, SCM y)
{
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      return SCM_BOOL (xx == yy);
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL_F;
    } else if (SCM_REALP (y)) {
      return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y))
                       && (0.0 == SCM_COMPLEX_IMAG (y)));
    } else {
      SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BOOL_F;
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL (0 == scm_bigcomp (x, y));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL (scm_i_big2dbl (x) == SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return SCM_BOOL ((scm_i_big2dbl (x) == SCM_COMPLEX_REAL (y))
                       && (0.0 == SCM_COMPLEX_IMAG (y)));
    } else {
      SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y));
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) == scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y))
                       && (0.0 == SCM_COMPLEX_IMAG (y)));
    } else {
      SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
    }
  } else if (SCM_COMPLEXP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y))
                       && (SCM_COMPLEX_IMAG (x) == 0.0));
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL ((SCM_COMPLEX_REAL (x) == scm_i_big2dbl (y))
                       && (SCM_COMPLEX_IMAG (x) == 0.0));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y))
                       && (SCM_COMPLEX_IMAG (x) == 0.0));
    } else if (SCM_COMPLEXP (y)) {
      return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y))
                       && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)));
    } else {
      SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p);
  }
}


SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p);
/* "Return @code{#t} if the list of parameters is monotonically\n"
 * "increasing."
 */
SCM
scm_less_p (SCM x, SCM y)
{
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      return SCM_BOOL (xx < yy);
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL (!SCM_BIGSIGN (y));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BOOL (SCM_BIGSIGN (x));
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL (1 == scm_bigcomp (x, y));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL (scm_i_big2dbl (x) < SCM_REAL_VALUE (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y));
    } else if (SCM_BIGP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) < scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p);
  }
}


SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p);
/* "Return @code{#t} if the list of parameters is monotonically\n"
 * "decreasing."
 */
#define FUNC_NAME s_scm_gr_p
SCM
scm_gr_p (SCM x, SCM y)
{
  if (!SCM_NUMBERP (x))
    SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME);
  else if (!SCM_NUMBERP (y))
    SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME);
  else
    return scm_less_p (y, x);
}
#undef FUNC_NAME


SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p);
/* "Return @code{#t} if the list of parameters is monotonically\n"
 * "non-decreasing."
 */
#define FUNC_NAME s_scm_leq_p
SCM
scm_leq_p (SCM x, SCM y)
{
  if (!SCM_NUMBERP (x))
    SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME);
  else if (!SCM_NUMBERP (y))
    SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME);
  else
    return SCM_BOOL_NOT (scm_less_p (y, x));
}
#undef FUNC_NAME


SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p);
/* "Return @code{#t} if the list of parameters is monotonically\n"
 * "non-increasing."
 */
#define FUNC_NAME s_scm_geq_p
SCM
scm_geq_p (SCM x, SCM y)
{
  if (!SCM_NUMBERP (x))
    SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME);
  else if (!SCM_NUMBERP (y))
    SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME);
  else
  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);
/* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n"
 * "zero."
 */
SCM
scm_zero_p (SCM z)
{
  if (SCM_INUMP (z)) {
    return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0));
  } else if (SCM_BIGP (z)) {
    return SCM_BOOL_F;
  } else if (SCM_REALP (z)) {
    return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0);
  } else if (SCM_COMPLEXP (z)) {
    return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0
                     && SCM_COMPLEX_IMAG (z) == 0.0);
  } else {
    SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p);
  }
}


SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p);
/* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n"
 * "zero."
 */
SCM
scm_positive_p (SCM x)
{
  if (SCM_INUMP (x)) {
    return SCM_BOOL (SCM_INUM (x) > 0);
  } else if (SCM_BIGP (x)) {
    return SCM_BOOL (!SCM_BIGSIGN (x));
  } else if (SCM_REALP (x)) {
    return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0);
  } else {
    SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p);
  }
}


SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p);
/* "Return @code{#t} if @var{x} is an exact or inexact number less than\n"
 * "zero."
 */
SCM
scm_negative_p (SCM x)
{
  if (SCM_INUMP (x)) {
    return SCM_BOOL (SCM_INUM (x) < 0);
  } else if (SCM_BIGP (x)) {
    return SCM_BOOL (SCM_BIGSIGN (x));
  } else if (SCM_REALP (x)) {
    return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0);
  } else {
    SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p);
  }
}


SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max);
/* "Return the maximum of all parameter values."
 */
SCM
scm_max (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      SCM_WTA_DISPATCH_0 (g_max, s_max);
    } else if (SCM_NUMBERP (x)) {
      return x;
    } else {
      SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max);
    }
  }
  
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      return (xx < yy) ? y : x;
    } else if (SCM_BIGP (y)) {
      return SCM_BIGSIGN (y) ? x : y;
    } else if (SCM_REALP (y)) {
      double z = xx;
      return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z);
    } else {
      SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BIGSIGN (x) ? y : x;
    } else if (SCM_BIGP (y)) {
      return (1 == scm_bigcomp (x, y)) ? y : x;
    } else if (SCM_REALP (y)) {
      double z = scm_i_big2dbl (x);
      return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z);
    } else {
      SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      double z = SCM_INUM (y);
      return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x;
    } else if (SCM_BIGP (y)) {
      double z = scm_i_big2dbl (y);
      return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x;
    } else if (SCM_REALP (y)) {
      return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? y : x;
    } else {
      SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max);
  }
}


SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min);
/* "Return the minium of all parameter values."
 */
SCM
scm_min (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      SCM_WTA_DISPATCH_0 (g_min, s_min);
    } else if (SCM_NUMBERP (x)) {
      return x;
    } else {
      SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min);
    }
  }
  
  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      return (xx < yy) ? x : y;
    } else if (SCM_BIGP (y)) {
      return SCM_BIGSIGN (y) ? y : x;
    } else if (SCM_REALP (y)) {
      double z = xx;
      return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
    } else {
      SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      return SCM_BIGSIGN (x) ? x : y;
    } else if (SCM_BIGP (y)) {
      return (-1 == scm_bigcomp (x, y)) ? y : x;
    } else if (SCM_REALP (y)) {
      double z = scm_i_big2dbl (x);
      return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
    } else {
      SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      double z = SCM_INUM (y);
      return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z);
    } else if (SCM_BIGP (y)) {
      double z = scm_i_big2dbl (y);
      return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z);
    } else if (SCM_REALP (y)) {
      return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? x : y;
    } else {
      SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min);
  }
}


SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum);
/* "Return the sum of all parameter values.  Return 0 if called without\n"
 * "any parameters." 
 */
SCM
scm_sum (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      return SCM_INUM0;
    } else if (SCM_NUMBERP (x)) {
      return x;
    } else {
      SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum);
    }
  }

  if (SCM_INUMP (x)) {
    long int xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
      long int z = xx + yy;
      if (SCM_FIXABLE (z)) {
        return SCM_MAKINUM (z);
      } else {
#ifdef SCM_BIGDIG
        return scm_i_long2big (z);
#else  /* SCM_BIGDIG */
        return scm_make_real ((double) z);
#endif /* SCM_BIGDIG */ 
      }
    } else if (SCM_BIGP (y)) {
    intbig:
      {
        long int xx = SCM_INUM (x);
#ifndef SCM_DIGSTOOBIG
        long z = scm_pseudolong (xx);
        return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
                           (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0);
#else  /* SCM_DIGSTOOBIG */
        SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
        scm_longdigs (xx, zdigs);
        return scm_addbig (zdigs, SCM_DIGSPERLONG, 
                           (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0);
#endif /* SCM_DIGSTOOBIG */
      }
    } else if (SCM_REALP (y)) {
      return scm_make_real (xx + SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (xx + SCM_COMPLEX_REAL (y),
                               SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      SCM_SWAP (x, y);
      goto intbig;
    } else if (SCM_BIGP (y)) {
      if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) {
        SCM_SWAP (x, y);
      }
      return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), 
                         SCM_BIGSIGN (x), y, 0);
    } else if (SCM_REALP (y)) {
      return scm_make_real (scm_i_big2dbl (x) + SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (scm_i_big2dbl (x) + SCM_COMPLEX_REAL (y),
                               SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y));
    } else if (SCM_BIGP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) + scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
                               SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
    }
  } else if (SCM_COMPLEXP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_BIGP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_big2dbl (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_REALP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y),
                               SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum);
  }
}


SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference);
/* If called with one argument @var{z1}, -@var{z1} returned. Otherwise
 * the sum of all but the first argument are subtracted from the first
 * argument.  */
#define FUNC_NAME s_difference
SCM
scm_difference (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      SCM_WTA_DISPATCH_0 (g_difference, s_difference);
    } else if (SCM_INUMP (x)) {
      long xx = -SCM_INUM (x);
      if (SCM_FIXABLE (xx)) {
        return SCM_MAKINUM (xx);
      } else {
#ifdef SCM_BIGDIG
        return scm_i_long2big (xx);
#else
        return scm_make_real ((double) xx);
#endif
      }
    } else if (SCM_BIGP (x)) {
      SCM z = scm_i_copybig (x, !SCM_BIGSIGN (x));
      unsigned int digs = SCM_NUMDIGS (z);
      unsigned int size = digs * SCM_BITSPERDIG / SCM_CHAR_BIT;
      return size <= sizeof (SCM) ? scm_i_big2inum (z, digs) : z;
    } else if (SCM_REALP (x)) {
      return scm_make_real (-SCM_REAL_VALUE (x));
    } else if (SCM_COMPLEXP (x)) {
      return scm_make_complex (-SCM_COMPLEX_REAL (x), -SCM_COMPLEX_IMAG (x));
    } else {
      SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference);
    }
  }

  if (SCM_INUMP (x)) {
    long int xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
      long int z = xx - yy;
      if (SCM_FIXABLE (z)) {
        return SCM_MAKINUM (z);
      } else {
#ifdef SCM_BIGDIG
        return scm_i_long2big (z);
#else
        return scm_make_real ((double) z);
#endif
      }
    } else if (SCM_BIGP (y)) {
#ifndef SCM_DIGSTOOBIG
      long z = scm_pseudolong (xx);
      return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
                         (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG);
#else
      SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
      scm_longdigs (xx, zdigs);
      return scm_addbig (zdigs, SCM_DIGSPERLONG, 
                         (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG);
#endif
    } else if (SCM_REALP (y)) {
      return scm_make_real (xx - SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (xx - SCM_COMPLEX_REAL (y),
                               -SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
#ifndef SCM_DIGSTOOBIG
      long z = scm_pseudolong (yy);
      return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
                         (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0);
#else
      SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
      scm_longdigs (yy, zdigs);
      return scm_addbig (zdigs, SCM_DIGSPERLONG, 
                         (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0);
#endif
    } else if (SCM_BIGP (y)) {
      return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y))
        ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                      SCM_BIGSIGN (x), y, SCM_BIGSIGNFLAG)
        : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y),
                      SCM_BIGSIGN (y) ^ SCM_BIGSIGNFLAG, x, 0);
    } else if (SCM_REALP (y)) {
      return scm_make_real (scm_i_big2dbl (x) - SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (scm_i_big2dbl (x) - SCM_COMPLEX_REAL (y),
                               - SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y));
    } else if (SCM_BIGP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) - scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
                               -SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
    }
  } else if (SCM_COMPLEXP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_BIGP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_big2dbl (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_REALP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y),
                               SCM_COMPLEX_IMAG (x));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y),
                               SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference);
  }
}
#undef FUNC_NAME

SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product);
/* "Return the product of all arguments.  If called without arguments,\n"
 * "1 is returned."
 */
SCM
scm_product (SCM x, SCM y)
{
  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      return SCM_MAKINUM (1L);
    } else if (SCM_NUMBERP (x)) {
      return x;
    } else {
      SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product);
    }
  }

  if (SCM_INUMP (x)) {
    long xx;

  intbig:
    xx = SCM_INUM (x);

    if (xx == 0) {
      return x;
    } else if (xx == 1) {
      return y;
    }

    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      long kk = xx * yy;
      SCM k = SCM_MAKINUM (kk);
      if (kk != SCM_INUM (k) || kk / xx != yy) {
#ifdef SCM_BIGDIG
        int sgn = (xx < 0) ^ (yy < 0);
#ifndef SCM_DIGSTOOBIG
        long i = scm_pseudolong (xx);
        long j = scm_pseudolong (yy);
        return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG,
                           (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn);
#else /* SCM_DIGSTOOBIG */
        SCM_BIGDIG xdigs [SCM_DIGSPERLONG];
        SCM_BIGDIG ydigs [SCM_DIGSPERLONG];
        scm_longdigs (xx, xdigs);
        scm_longdigs (yy, ydigs);
        return scm_mulbig (xdigs, SCM_DIGSPERLONG,
                           ydigs, SCM_DIGSPERLONG,
                           sgn);
#endif
#else
        return scm_make_real (((double) xx) * ((double) yy));
#endif
      } else {
        return k;
      }
    } else if (SCM_BIGP (y)) {
#ifndef SCM_DIGSTOOBIG
      long z = scm_pseudolong (xx);
      return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
                         SCM_BDIGITS (y), SCM_NUMDIGS (y),
                         SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0));
#else
      SCM_BIGDIG zdigs [SCM_DIGSPERLONG];
      scm_longdigs (xx, zdigs);
      return scm_mulbig (zdigs, SCM_DIGSPERLONG,
                         SCM_BDIGITS (y), SCM_NUMDIGS (y),
                         SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0));
#endif
    } else if (SCM_REALP (y)) {
      return scm_make_real (xx * SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
                               xx * SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      SCM_SWAP (x, y);
      goto intbig;
    } else 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));
    } else if (SCM_REALP (y)) {
      return scm_make_real (scm_i_big2dbl (x) * SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      double z = scm_i_big2dbl (x);
      return scm_make_complex (z * SCM_COMPLEX_REAL (y),
                               z * SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
    }
  } else if (SCM_REALP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x));
    } else if (SCM_BIGP (y)) {
      return scm_make_real (scm_i_big2dbl (y) * SCM_REAL_VALUE (x));
    } else if (SCM_REALP (y)) {
      return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
                               SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
    }
  } else if (SCM_COMPLEXP (x)) {
    if (SCM_INUMP (y)) {
      return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x),
                               SCM_INUM (y) * SCM_COMPLEX_IMAG (x));
    } else if (SCM_BIGP (y)) {
      double z = scm_i_big2dbl (y);
      return scm_make_complex (z * SCM_COMPLEX_REAL (x),
                               z * SCM_COMPLEX_IMAG (x));
    } else if (SCM_REALP (y)) {
      return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x),
                               SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x));
    } else if (SCM_COMPLEXP (y)) {
      return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y)
                               - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y),
                               SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y)
                               + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y));
    } else {
      SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product);
  }
}


double
scm_num2dbl (SCM a, const char *why)
#define FUNC_NAME why
{
  if (SCM_INUMP (a)) {
    return (double) SCM_INUM (a);
  } else if (SCM_BIGP (a)) {
    return scm_i_big2dbl (a);
  } else if (SCM_REALP (a)) {
    return (SCM_REAL_VALUE (a));
  } else {
    SCM_WRONG_TYPE_ARG (SCM_ARGn, a);
  }
}
#undef FUNC_NAME


/* The code below for complex division is adapted from the GNU
   libstdc++, which adapted it from f2c's libF77, and is subject to
   this copyright:  */

/****************************************************************
Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore.

Permission to use, copy, modify, and distribute this software
and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all
copies and that both that the copyright notice and this
permission notice and warranty disclaimer appear in supporting
documentation, and that the names of AT&T Bell Laboratories or
Bellcore or any of their entities not be used in advertising or
publicity pertaining to distribution of the software without
specific, written prior permission.

AT&T and Bellcore disclaim all warranties with regard to this
software, including all implied warranties of merchantability
and fitness.  In no event shall AT&T or Bellcore be liable for
any special, indirect or consequential damages or any damages
whatsoever resulting from loss of use, data or profits, whether
in an action of contract, negligence or other tortious action,
arising out of or in connection with the use or performance of
this software.
****************************************************************/

SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide);
/* Divide the first argument by the product of the remaining
   arguments.  If called with one argument @var{z1}, 1/@var{z1} is
   returned.  */
#define FUNC_NAME s_divide
SCM
scm_divide (SCM x, SCM y)
{
  double a;

  if (SCM_UNBNDP (y)) {
    if (SCM_UNBNDP (x)) {
      SCM_WTA_DISPATCH_0 (g_divide, s_divide);
    } else if (SCM_INUMP (x)) {
      long xx = SCM_INUM (x);
      if (xx == 1 || xx == -1) {
        return x;
      } else if (xx == 0) {
        scm_num_overflow (s_divide);
      } else {
        return scm_make_real (1.0 / (double) xx);
      }
    } else if (SCM_BIGP (x)) {
      return scm_make_real (1.0 / scm_i_big2dbl (x));
    } else if (SCM_REALP (x)) {
      double xx = SCM_REAL_VALUE (x);
      if (xx == 0.0)
        scm_num_overflow (s_divide);
      else
        return scm_make_real (1.0 / xx);
    } else if (SCM_COMPLEXP (x)) {
      double r = SCM_COMPLEX_REAL (x);
      double i = SCM_COMPLEX_IMAG (x);
      if (r <= i) {
        double t = r / i;
        double d = i * (1.0 + t * t);
        return scm_make_complex (t / d, -1.0 / d);
      } else {
        double t = i / r;
        double d = r * (1.0 + t * t);
        return scm_make_complex (1.0 / d, -t / d);
      }
    } else {
      SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
    }
  }

  if (SCM_INUMP (x)) {
    long xx = SCM_INUM (x);
    if (SCM_INUMP (y)) {
      long yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_divide);
      } else if (xx % yy != 0) {
        return scm_make_real ((double) xx / (double) yy);
      } else {
        long z = xx / yy;
        if (SCM_FIXABLE (z)) {
          return SCM_MAKINUM (z);
        } else {
#ifdef SCM_BIGDIG
          return scm_i_long2big (z);
#else
          return scm_make_real ((double) xx / (double) yy);
#endif
        }
      }
    } else if (SCM_BIGP (y)) {
      return scm_make_real ((double) xx / scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      double yy = SCM_REAL_VALUE (y);
      if (yy == 0.0)
        scm_num_overflow (s_divide);
      else
        return scm_make_real ((double) xx / yy);
    } else if (SCM_COMPLEXP (y)) {
      a = xx;
    complex_div: /* y _must_ be a complex number */
      {
        double r = SCM_COMPLEX_REAL (y);
        double i = SCM_COMPLEX_IMAG (y);
        if (r <= i) {
          double t = r / i;
          double d = i * (1.0 + t * t);
          return scm_make_complex ((a * t) / d,  -a / d);
        } else {
          double t = i / r;
          double d = r * (1.0 + t * t);
          return scm_make_complex (a / d,  -(a * t) / d);
        }
      }
    } else {
      SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
    }
  } else if (SCM_BIGP (x)) {
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_divide);
      } else if (yy == 1) {
        return x;
      } else {
        long z = yy < 0 ? -yy : yy;
        if (z < SCM_BIGRAD) {
          SCM w = scm_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0));
          return scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w),
                                (SCM_BIGDIG) z)
            ? scm_make_real (scm_i_big2dbl (x) / (double) yy)
            : scm_i_normbig (w);
        } else {
          SCM w;
#ifndef SCM_DIGSTOOBIG
          z = scm_pseudolong (z);
          w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                             (SCM_BIGDIG *) & z, SCM_DIGSPERLONG,
                             SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3);
#else
          SCM_BIGDIG zdigs[SCM_DIGSPERLONG];
          scm_longdigs (z, zdigs);
          w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                             zdigs, SCM_DIGSPERLONG,
                             SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3);
#endif
          return (!SCM_UNBNDP (w)) 
            ? w 
            : scm_make_real (scm_i_big2dbl (x) / (double) yy);
        }
      }
    } else if (SCM_BIGP (y)) {
      SCM w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x),
                             SCM_BDIGITS (y), SCM_NUMDIGS (y),
                             SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3);
      return (!SCM_UNBNDP (w)) 
        ? w 
        : scm_make_real (scm_i_big2dbl (x) / scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      double yy = SCM_REAL_VALUE (y);
      if (yy == 0.0)
        scm_num_overflow (s_divide);
      else
        return scm_make_real (scm_i_big2dbl (x) / yy);
    } else if (SCM_COMPLEXP (y)) {
      a = scm_i_big2dbl (x);
      goto complex_div;
    } else {
      SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
    }
  } else if (SCM_REALP (x)) {
    double rx = SCM_REAL_VALUE (x);
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_divide);
      } else {
        return scm_make_real (rx / (double) yy);
      }
    } else if (SCM_BIGP (y)) {
      return scm_make_real (rx / scm_i_big2dbl (y));
    } else if (SCM_REALP (y)) {
      double yy = SCM_REAL_VALUE (y);
      if (yy == 0.0)
        scm_num_overflow (s_divide);
      else
        return scm_make_real (rx / yy);
    } else if (SCM_COMPLEXP (y)) {
      a = rx;
      goto complex_div;
    } else {
      SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
    }
  } else if (SCM_COMPLEXP (x)) {
    double rx = SCM_COMPLEX_REAL (x);
    double ix = SCM_COMPLEX_IMAG (x);
    if (SCM_INUMP (y)) {
      long int yy = SCM_INUM (y);
      if (yy == 0) {
        scm_num_overflow (s_divide);
      } else {
        double d = yy;
        return scm_make_complex (rx / d, ix / d);
      }
    } else if (SCM_BIGP (y)) {
      double d = scm_i_big2dbl (y);
      return scm_make_complex (rx / d, ix / d);
    } else if (SCM_REALP (y)) {
      double yy = SCM_REAL_VALUE (y);
      if (yy == 0.0)
        scm_num_overflow (s_divide);
      else
        return scm_make_complex (rx / yy, ix / yy);
    } else if (SCM_COMPLEXP (y)) {
      double ry = SCM_COMPLEX_REAL (y);
      double iy = SCM_COMPLEX_IMAG (y);
      if (ry <= iy) {
        double t = ry / iy;
        double d = iy * (1.0 + t * t);
        return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d);
      } else {
        double t = iy / ry;
        double d = ry * (1.0 + t * t);
        return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d);
      }
    } else {
      SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
    }
  } else {
    SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide);
  }
}
#undef FUNC_NAME

SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh);
/* "Return the inverse hyperbolic sine of @var{x}."
 */
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);
/* "Return the inverse hyperbolic cosine of @var{x}."
 */
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);
/* "Return the inverse hyperbolic tangent of @var{x}."
 */
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);
/* "Round the inexact number @var{x} towards zero."
 */
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);
/* "Round the inexact number @var{x}. If @var{x} is halfway between two\n"
 * "numbers, round towards even."
 */
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_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor);
/* "Round the number @var{x} towards minus infinity."
 */
SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil);
/* "Round the number @var{x} towards infinity."
 */
SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt);
/* "Return the square root of the real number @var{x}."
 */
SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs);
/* "Return the absolute value of the real number @var{x}."
 */
SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp);
/* "Return the @var{x}th power of e."
 */
SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log);
/* "Return the natural logarithm of the real number @var{x}."
 */
SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin);
/* "Return the sine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos);
/* "Return the cosine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan);
/* "Return the tangent of the real number @var{x}."
 */
SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin);
/* "Return the arc sine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos);
/* "Return the arc cosine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan);
/* "Return the arc tangent of the real number @var{x}."
 */
SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh);
/* "Return the hyperbolic sine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh);
/* "Return the hyperbolic cosine of the real number @var{x}."
 */
SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh);
/* "Return the hyperbolic tangent of the real number @var{x}."
 */

struct dpair
{
  double x, y;
};

static void scm_two_doubles (SCM x,
                             SCM y,
                             const char *sstring,
                             struct dpair * xy);

static void
scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy)
{
  if (SCM_INUMP (x)) {
    xy->x = SCM_INUM (x);
  } else if (SCM_BIGP (x)) {
    xy->x = scm_i_big2dbl (x);
  } else if (SCM_REALP (x)) {
    xy->x = SCM_REAL_VALUE (x);
  } else {
    scm_wrong_type_arg (sstring, SCM_ARG1, x);
  }

  if (SCM_INUMP (y)) {
    xy->y = SCM_INUM (y);
  } else if (SCM_BIGP (y)) {
    xy->y = scm_i_big2dbl (y);
  } else if (SCM_REALP (y)) {
    xy->y = SCM_REAL_VALUE (y);
  } else {
    scm_wrong_type_arg (sstring, SCM_ARG2, y);
  }
}


SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0,
            (SCM x, SCM y),
            "Return @var{x} raised to the power of @var{y}. This\n"
            "procedure does not accept complex arguments.") 
#define FUNC_NAME s_scm_sys_expt
{
  struct dpair xy;
  scm_two_doubles (x, y, FUNC_NAME, &xy);
  return scm_make_real (pow (xy.x, xy.y));
}
#undef FUNC_NAME


SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0,
            (SCM x, SCM y),
            "Return the arc tangent of the two arguments @var{x} and\n"
            "@var{y}. This is similar to calculating the arc tangent of\n"
            "@var{x} / @var{y}, except that the signs of both arguments\n"
            "are used to determine the quadrant of the result. This\n"
            "procedure does not accept complex arguments.")
#define FUNC_NAME s_scm_sys_atan2
{
  struct dpair xy;
  scm_two_doubles (x, y, FUNC_NAME, &xy);
  return scm_make_real (atan2 (xy.x, xy.y));
}
#undef FUNC_NAME


SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0,
            (SCM real, SCM imaginary),
            "Return a complex number constructed of the given @var{real} and\n"
            "@var{imaginary} parts.")
#define FUNC_NAME s_scm_make_rectangular
{
  struct dpair xy;
  scm_two_doubles (real, imaginary, FUNC_NAME, &xy);
  return scm_make_complex (xy.x, xy.y);
}
#undef FUNC_NAME



SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0,
            (SCM x, SCM y),
            "Return the complex number @var{x} * e^(i * @var{y}).")
#define FUNC_NAME s_scm_make_polar
{
  struct dpair xy;
  scm_two_doubles (x, y, FUNC_NAME, &xy);
  return scm_make_complex (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);
/* "Return the real part of the number @var{z}."
 */
SCM
scm_real_part (SCM z)
{
  if (SCM_INUMP (z)) {
    return z;
  } else if (SCM_BIGP (z)) {
    return z;
  } else if (SCM_REALP (z)) {
    return z;
  } else if (SCM_COMPLEXP (z)) {
    return scm_make_real (SCM_COMPLEX_REAL (z));
  } else {
    SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part);
  }
}


SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part);
/* "Return the imaginary part of the number @var{z}."
 */
SCM
scm_imag_part (SCM z)
{
  if (SCM_INUMP (z)) {
    return SCM_INUM0;
  } else if (SCM_BIGP (z)) {
    return SCM_INUM0;
  } else if (SCM_REALP (z)) {
    return scm_flo0;
  } else if (SCM_COMPLEXP (z)) {
    return scm_make_real (SCM_COMPLEX_IMAG (z));
  } else {
    SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part);
  }
}


SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude);
/* "Return the magnitude of the number @var{z}. This is the same as\n"
 * "@code{abs} for real arguments, but also allows complex numbers."
 */
SCM
scm_magnitude (SCM z)
{
  if (SCM_INUMP (z)) {
    long int zz = SCM_INUM (z);
    if (zz >= 0) {
      return z;
    } else if (SCM_POSFIXABLE (-zz)) {
      return SCM_MAKINUM (-zz);
    } else {
#ifdef SCM_BIGDIG
      return scm_i_long2big (-zz);
#else
      scm_num_overflow (s_magnitude);
#endif
    }
  } else if (SCM_BIGP (z)) {
    if (!SCM_BIGSIGN (z)) {
      return z;
    } else {
      return scm_i_copybig (z, 0);
    }
  } else if (SCM_REALP (z)) {
    return scm_make_real (fabs (SCM_REAL_VALUE (z)));
  } else if (SCM_COMPLEXP (z)) {
    double r = SCM_COMPLEX_REAL (z);
    double i = SCM_COMPLEX_IMAG (z);
    return scm_make_real (sqrt (i * i + r * r));
  } else {
    SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude);
  }
}


SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle);
/* "Return the angle of the complex number @var{z}."
 */
SCM
scm_angle (SCM z)
{
  if (SCM_INUMP (z)) {
    if (SCM_INUM (z) >= 0) {
      return scm_make_real (atan2 (0.0, 1.0));
    } else {
      return scm_make_real (atan2 (0.0, -1.0));
    }
  } else if (SCM_BIGP (z)) {
    if (SCM_BIGSIGN (z)) {
      return scm_make_real (atan2 (0.0, -1.0));
    } else {
      return scm_make_real (atan2 (0.0, 1.0));
    }
  } else if (SCM_REALP (z)) {
    return scm_make_real (atan2 (0.0, SCM_REAL_VALUE (z)));
  } else if (SCM_COMPLEXP (z)) {
    return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z)));
  } else {
    SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle);
  }
}


SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact);
/* Convert the number @var{x} to its inexact representation.\n" 
 */
SCM
scm_exact_to_inexact (SCM z)
{
  if (SCM_INUMP (z))
    return scm_make_real ((double) SCM_INUM (z));
  else if (SCM_BIGP (z))
    return scm_make_real (scm_i_big2dbl (z));
  else if (SCM_INEXACTP (z))
    return z;
  else
    SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact);
}


SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, 
            (SCM z),
            "Return an exact number that is numerically closest to @var{z}.")
#define FUNC_NAME s_scm_inexact_to_exact
{
  if (SCM_INUMP (z)) {
    return z;
  } else if (SCM_BIGP (z)) {
    return z;
  } else if (SCM_REALP (z)) {
    double u = floor (SCM_REAL_VALUE (z) + 0.5);
    long lu = (long) u;
    if (SCM_FIXABLE (lu)) {
      return SCM_MAKINUM (lu);
#ifdef SCM_BIGDIG
    } else if (isfinite (u)) {
      return scm_i_dbl2big (u);
#endif
    } else {
      scm_num_overflow (s_scm_inexact_to_exact);
    }
  } else {
    SCM_WRONG_TYPE_ARG (1, z);
  }
}
#undef FUNC_NAME


#ifdef SCM_BIGDIG
/* d must be integer */

SCM
scm_i_dbl2big (double d)
{
  size_t 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_i_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_i_big2dbl (SCM b)
{
  double ans = 0.0;
  size_t i = SCM_NUMDIGS (b);
  SCM_BIGDIG *digits = SCM_BDIGITS (b);
  while (i--)
    ans = digits[i] + SCM_BIGRAD * ans;
  if (SCM_BIGSIGN (b))
    return - ans;
  return ans;
}

#endif

#ifdef HAVE_LONG_LONGS
# ifndef LLONG_MAX
#  define ULLONG_MAX ((unsigned long long) (-1))
#  define LLONG_MAX ((long long) (ULLONG_MAX >> 1))
#  define LLONG_MIN (~LLONG_MAX)
# endif
#endif

/* Parameters for creating integer conversion routines.

   Define the following preprocessor macros before including
   "libguile/num2integral.i.c":

   NUM2INTEGRAL - the name of the function for converting from a
                  Scheme object to the integral type.  This function
                  will be defined when including "num2integral.i.c".

   INTEGRAL2NUM - the name of the function for converting from the
                  integral type to a Scheme object.  This function
                  will be defined.

   INTEGRAL2BIG - the name of an internal function that createas a
                  bignum from the integral type.  This function will
                  be defined.  The name should start with "scm_i_".

   ITYPE        - the name of the integral type.

   UNSIGNED     - Define this when ITYPE is an unsigned type.  Do not
                  define it otherwise.

   UNSIGNED_ITYPE
                - the name of the the unsigned variant of the
                  integral type.  If you don't define this, it defaults
                  to "unsigned ITYPE" for signed types and simply "ITYPE"
                  for unsigned ones.

   SIZEOF_ITYPE - an expression giving the size of the integral type in
                  bytes.  This expression must be computable by the
                  preprocessor.  If you don't know a value for this,
                  don't define it.  The purpose of this parameter is
                  mainly to suppress some warnings.  The generated
                  code will work correctly without it.
*/

#define NUM2INTEGRAL scm_num2short
#define INTEGRAL2NUM scm_short2num
#define INTEGRAL2BIG scm_i_short2big
#define ITYPE short
#define SIZEOF_ITYPE SIZEOF_SHORT
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2ushort
#define INTEGRAL2NUM scm_ushort2num
#define INTEGRAL2BIG scm_i_ushort2big
#define UNSIGNED
#define ITYPE unsigned short
#define SIZEOF_ITYPE SIZEOF_SHORT
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2int
#define INTEGRAL2NUM scm_int2num
#define INTEGRAL2BIG scm_i_int2big
#define ITYPE int
#define SIZEOF_ITYPE SIZEOF_INT
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2uint
#define INTEGRAL2NUM scm_uint2num
#define INTEGRAL2BIG scm_i_uint2big
#define UNSIGNED
#define ITYPE unsigned int
#define SIZEOF_ITYPE SIZEOF_INT
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2long
#define INTEGRAL2NUM scm_long2num
#define INTEGRAL2BIG scm_i_long2big
#define ITYPE long
#define SIZEOF_ITYPE SIZEOF_LONG
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2ulong
#define INTEGRAL2NUM scm_ulong2num
#define INTEGRAL2BIG scm_i_ulong2big
#define UNSIGNED
#define ITYPE unsigned long
#define SIZEOF_ITYPE SIZEOF_LONG
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2ptrdiff
#define INTEGRAL2NUM scm_ptrdiff2num
#define INTEGRAL2BIG scm_i_ptrdiff2big
#define ITYPE ptrdiff_t
#define UNSIGNED_ITYPE size_t
#define SIZEOF_ITYPE SIZEOF_PTRDIFF_T
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2size
#define INTEGRAL2NUM scm_size2num
#define INTEGRAL2BIG scm_i_size2big
#define UNSIGNED
#define ITYPE size_t
#define SIZEOF_ITYPE SIZEOF_SIZE_T
#include "libguile/num2integral.i.c"

#ifdef HAVE_LONG_LONGS

#ifndef ULONG_LONG_MAX
#define ULONG_LONG_MAX (~0ULL)
#endif

#define NUM2INTEGRAL scm_num2long_long
#define INTEGRAL2NUM scm_long_long2num
#define INTEGRAL2BIG scm_i_long_long2big
#define ITYPE long long
#define SIZEOF_ITYPE SIZEOF_LONG_LONG
#include "libguile/num2integral.i.c"

#define NUM2INTEGRAL scm_num2ulong_long
#define INTEGRAL2NUM scm_ulong_long2num
#define INTEGRAL2BIG scm_i_ulong_long2big
#define UNSIGNED
#define ITYPE unsigned long long
#define SIZEOF_ITYPE SIZEOF_LONG_LONG
#include "libguile/num2integral.i.c"

#endif /* HAVE_LONG_LONGS */

#define NUM2FLOAT scm_num2float
#define FLOAT2NUM scm_float2num
#define FTYPE float
#include "libguile/num2float.i.c"

#define NUM2FLOAT scm_num2double
#define FLOAT2NUM scm_double2num
#define FTYPE double
#include "libguile/num2float.i.c"

#ifdef GUILE_DEBUG

#ifndef SIZE_MAX
#define SIZE_MAX ((size_t) (-1))
#endif
#ifndef PTRDIFF_MIN
#define PTRDIFF_MIN \
 ((ptrdiff_t) ((ptrdiff_t) 1 << (sizeof (ptrdiff_t) * 8 - 1)))
#endif
#ifndef PTRDIFF_MAX
#define PTRDIFF_MAX (~ PTRDIFF_MIN)
#endif

#define CHECK(type, v) \
  do { \
    if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \
      abort (); \
  } while (0);

static void
check_sanity ()
{
  CHECK (short, 0);
  CHECK (ushort, 0U);
  CHECK (int, 0);
  CHECK (uint, 0U);
  CHECK (long, 0L);
  CHECK (ulong, 0UL);
  CHECK (size, 0);
  CHECK (ptrdiff, 0);

  CHECK (short, -1);
  CHECK (int, -1);
  CHECK (long, -1L);
  CHECK (ptrdiff, -1);

  CHECK (short, SHRT_MAX);
  CHECK (short, SHRT_MIN);
  CHECK (ushort, USHRT_MAX);
  CHECK (int, INT_MAX);
  CHECK (int, INT_MIN);
  CHECK (uint, UINT_MAX);
  CHECK (long, LONG_MAX);
  CHECK (long, LONG_MIN);
  CHECK (ulong, ULONG_MAX);
  CHECK (size, SIZE_MAX);
  CHECK (ptrdiff, PTRDIFF_MAX);
  CHECK (ptrdiff, PTRDIFF_MIN);

#ifdef HAVE_LONG_LONGS
  CHECK (long_long, 0LL);
  CHECK (ulong_long, 0ULL);
  CHECK (long_long, -1LL);
  CHECK (long_long, LLONG_MAX);
  CHECK (long_long, LLONG_MIN);
  CHECK (ulong_long, ULLONG_MAX);
#endif
}

#undef CHECK

#define CHECK \
        scm_internal_catch (SCM_BOOL_T, check_body, &data, check_handler, &data); \
        if (!SCM_FALSEP (data)) abort();

static SCM
check_body (void *data)
{
  SCM num = *(SCM *) data;
  scm_num2ulong (num, 1, NULL);
  
  return SCM_UNSPECIFIED;
}

static SCM
check_handler (void *data, SCM tag, SCM throw_args)
{
  SCM *num = (SCM *) data;
  *num = SCM_BOOL_F;

  return SCM_UNSPECIFIED;
}
  
SCM_DEFINE (scm_sys_check_number_conversions, "%check-number-conversions", 0, 0, 0, 
            (void),
            "Number conversion sanity checking.")
#define FUNC_NAME s_scm_sys_check_number_conversions
{
  SCM data = SCM_MAKINUM (-1);
  CHECK;
  data = scm_int2num (INT_MIN);
  CHECK;
  data = scm_ulong2num (ULONG_MAX);
  data = scm_difference (SCM_INUM0, data);
  CHECK;
  data = scm_ulong2num (ULONG_MAX);
  data = scm_sum (SCM_MAKINUM (1), data); data = scm_difference (SCM_INUM0, data);
  CHECK;
  data = scm_int2num (-10000); data = scm_product (data, data); data = scm_product (data, data);
  CHECK;

  return SCM_UNSPECIFIED;
}
#undef FUNC_NAME

#endif

void
scm_init_numbers ()
{
  abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM);
  scm_permanent_object (abs_most_negative_fixnum);

  /* It may be possible to tune the performance of some algorithms by using
   * the following constants to avoid the creation of bignums.  Please, before
   * using these values, remember the two rules of program optimization:
   * 1st Rule:  Don't do it.  2nd Rule (experts only):  Don't do it yet. */
  scm_c_define ("most-positive-fixnum",
                SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM));
  scm_c_define ("most-negative-fixnum",
                SCM_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM));

  scm_add_feature ("complex");
  scm_add_feature ("inexact");
  scm_flo0 = scm_make_real (0.0);
#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) {
      if (++scm_dblprec > 20) {
        fsum = 1.0;
      } else {
        f /= 10.0;
        fsum = f + 1.0;
      }
    }
    scm_dblprec = scm_dblprec - 1;
  }
#endif /* DBL_DIG */

#ifdef GUILE_DEBUG
  check_sanity ();
#endif
  
#include "libguile/numbers.x"
}

/*
  Local Variables:
  c-file-style: "gnu"
  End:
*/