gcc/gcc/fortran/arith.c

/* Compiler arithmetic
   Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006
   Free Software Foundation, Inc.
   Contributed by Andy Vaught

This file is part of GCC.

GCC 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.

GCC 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 GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

/* Since target arithmetic must be done on the host, there has to
   be some way of evaluating arithmetic expressions as the host
   would evaluate them.  We use the GNU MP library and the MPFR
   library to do arithmetic, and this file provides the interface.  */

#include "config.h"
#include "system.h"
#include "flags.h"
#include "gfortran.h"
#include "arith.h"

/* MPFR does not have a direct replacement for mpz_set_f() from GMP.
   It's easily implemented with a few calls though.  */

void
gfc_mpfr_to_mpz (mpz_t z, mpfr_t x)
{
  mp_exp_t e;

  e = mpfr_get_z_exp (z, x);
  /* MPFR 2.0.1 (included with GMP 4.1) has a bug whereby mpfr_get_z_exp
     may set the sign of z incorrectly.  Work around that here.  */
  if (mpfr_sgn (x) != mpz_sgn (z))
    mpz_neg (z, z);

  if (e > 0)
    mpz_mul_2exp (z, z, e);
  else
    mpz_tdiv_q_2exp (z, z, -e);
}


/* Set the model number precision by the requested KIND.  */

void
gfc_set_model_kind (int kind)
{
  int index = gfc_validate_kind (BT_REAL, kind, false);
  int base2prec;

  base2prec = gfc_real_kinds[index].digits;
  if (gfc_real_kinds[index].radix != 2)
    base2prec *= gfc_real_kinds[index].radix / 2;
  mpfr_set_default_prec (base2prec);
}


/* Set the model number precision from mpfr_t x.  */

void
gfc_set_model (mpfr_t x)
{
  mpfr_set_default_prec (mpfr_get_prec (x));
}

#if MPFR_VERSION_MAJOR < 2 || (MPFR_VERSION_MAJOR == 2 && MPFR_VERSION_MINOR < 2)
/* Calculate atan2 (y, x)

atan2(y, x) = atan(y/x)				if x > 0,
	      sign(y)*(pi - atan(|y/x|))	if x < 0,
	      0					if x = 0 && y == 0,
	      sign(y)*pi/2			if x = 0 && y != 0.
*/

void
arctangent2 (mpfr_t y, mpfr_t x, mpfr_t result)
{
  int i;
  mpfr_t t;

  gfc_set_model (y);
  mpfr_init (t);

  i = mpfr_sgn (x);

  if (i > 0)
    {
      mpfr_div (t, y, x, GFC_RND_MODE);
      mpfr_atan (result, t, GFC_RND_MODE);
    }
  else if (i < 0)
    {
      mpfr_const_pi (result, GFC_RND_MODE);
      mpfr_div (t, y, x, GFC_RND_MODE);
      mpfr_abs (t, t, GFC_RND_MODE);
      mpfr_atan (t, t, GFC_RND_MODE);
      mpfr_sub (result, result, t, GFC_RND_MODE);
      if (mpfr_sgn (y) < 0)
	mpfr_neg (result, result, GFC_RND_MODE);
    }
  else
    {
      if (mpfr_sgn (y) == 0)
	mpfr_set_ui (result, 0, GFC_RND_MODE);
      else
	{
          mpfr_const_pi (result, GFC_RND_MODE);
          mpfr_div_ui (result, result, 2, GFC_RND_MODE);
	  if (mpfr_sgn (y) < 0)
	    mpfr_neg (result, result, GFC_RND_MODE);
	}
    }

  mpfr_clear (t);
}
#endif

/* Given an arithmetic error code, return a pointer to a string that
   explains the error.  */

static const char *
gfc_arith_error (arith code)
{
  const char *p;

  switch (code)
    {
    case ARITH_OK:
      p = _("Arithmetic OK at %L");
      break;
    case ARITH_OVERFLOW:
      p = _("Arithmetic overflow at %L");
      break;
    case ARITH_UNDERFLOW:
      p = _("Arithmetic underflow at %L");
      break;
    case ARITH_NAN:
      p = _("Arithmetic NaN at %L");
      break;
    case ARITH_DIV0:
      p = _("Division by zero at %L");
      break;
    case ARITH_INCOMMENSURATE:
      p = _("Array operands are incommensurate at %L");
      break;
    case ARITH_ASYMMETRIC:
      p =
	_("Integer outside symmetric range implied by Standard Fortran at %L");
      break;
    default:
      gfc_internal_error ("gfc_arith_error(): Bad error code");
    }

  return p;
}


/* Get things ready to do math.  */

void
gfc_arith_init_1 (void)
{
  gfc_integer_info *int_info;
  gfc_real_info *real_info;
  mpfr_t a, b, c;
  mpz_t r;
  int i;

  mpfr_set_default_prec (128);
  mpfr_init (a);
  mpz_init (r);

  /* Convert the minimum and maximum values for each kind into their
     GNU MP representation.  */
  for (int_info = gfc_integer_kinds; int_info->kind != 0; int_info++)
    {
      /* Huge  */
      mpz_set_ui (r, int_info->radix);
      mpz_pow_ui (r, r, int_info->digits);

      mpz_init (int_info->huge);
      mpz_sub_ui (int_info->huge, r, 1);

      /* These are the numbers that are actually representable by the
         target.  For bases other than two, this needs to be changed.  */
      if (int_info->radix != 2)
        gfc_internal_error ("Fix min_int calculation");

      /* See PRs 13490 and 17912, related to integer ranges.
         The pedantic_min_int exists for range checking when a program
         is compiled with -pedantic, and reflects the belief that
         Standard Fortran requires integers to be symmetrical, i.e.
         every negative integer must have a representable positive
         absolute value, and vice versa.  */

      mpz_init (int_info->pedantic_min_int);
      mpz_neg (int_info->pedantic_min_int, int_info->huge);

      mpz_init (int_info->min_int);
      mpz_sub_ui (int_info->min_int, int_info->pedantic_min_int, 1);

      /* Range  */
      mpfr_set_z (a, int_info->huge, GFC_RND_MODE);
      mpfr_log10 (a, a, GFC_RND_MODE);
      mpfr_trunc (a, a);
      gfc_mpfr_to_mpz (r, a);
      int_info->range = mpz_get_si (r);
    }

  mpfr_clear (a);

  for (real_info = gfc_real_kinds; real_info->kind != 0; real_info++)
    {
      gfc_set_model_kind (real_info->kind);

      mpfr_init (a);
      mpfr_init (b);
      mpfr_init (c);

      /* huge(x) = (1 - b**(-p)) * b**(emax-1) * b  */
      /* a = 1 - b**(-p)  */
      mpfr_set_ui (a, 1, GFC_RND_MODE);
      mpfr_set_ui (b, real_info->radix, GFC_RND_MODE);
      mpfr_pow_si (b, b, -real_info->digits, GFC_RND_MODE);
      mpfr_sub (a, a, b, GFC_RND_MODE);

      /* c = b**(emax-1)  */
      mpfr_set_ui (b, real_info->radix, GFC_RND_MODE);
      mpfr_pow_ui (c, b, real_info->max_exponent - 1, GFC_RND_MODE);

      /* a = a * c = (1 - b**(-p)) * b**(emax-1)  */
      mpfr_mul (a, a, c, GFC_RND_MODE);

      /* a = (1 - b**(-p)) * b**(emax-1) * b  */
      mpfr_mul_ui (a, a, real_info->radix, GFC_RND_MODE);

      mpfr_init (real_info->huge);
      mpfr_set (real_info->huge, a, GFC_RND_MODE);

      /* tiny(x) = b**(emin-1)  */
      mpfr_set_ui (b, real_info->radix, GFC_RND_MODE);
      mpfr_pow_si (b, b, real_info->min_exponent - 1, GFC_RND_MODE);

      mpfr_init (real_info->tiny);
      mpfr_set (real_info->tiny, b, GFC_RND_MODE);

      /* subnormal (x) = b**(emin - digit)  */
      mpfr_set_ui (b, real_info->radix, GFC_RND_MODE);
      mpfr_pow_si (b, b, real_info->min_exponent - real_info->digits,
		   GFC_RND_MODE);

      mpfr_init (real_info->subnormal);
      mpfr_set (real_info->subnormal, b, GFC_RND_MODE);

      /* epsilon(x) = b**(1-p)  */
      mpfr_set_ui (b, real_info->radix, GFC_RND_MODE);
      mpfr_pow_si (b, b, 1 - real_info->digits, GFC_RND_MODE);

      mpfr_init (real_info->epsilon);
      mpfr_set (real_info->epsilon, b, GFC_RND_MODE);

      /* range(x) = int(min(log10(huge(x)), -log10(tiny))  */
      mpfr_log10 (a, real_info->huge, GFC_RND_MODE);
      mpfr_log10 (b, real_info->tiny, GFC_RND_MODE);
      mpfr_neg (b, b, GFC_RND_MODE);

      /* a = min(a, b)  */
      if (mpfr_cmp (a, b) > 0)
	mpfr_set (a, b, GFC_RND_MODE);

      mpfr_trunc (a, a);
      gfc_mpfr_to_mpz (r, a);
      real_info->range = mpz_get_si (r);

      /* precision(x) = int((p - 1) * log10(b)) + k  */
      mpfr_set_ui (a, real_info->radix, GFC_RND_MODE);
      mpfr_log10 (a, a, GFC_RND_MODE);

      mpfr_mul_ui (a, a, real_info->digits - 1, GFC_RND_MODE);
      mpfr_trunc (a, a);
      gfc_mpfr_to_mpz (r, a);
      real_info->precision = mpz_get_si (r);

      /* If the radix is an integral power of 10, add one to the precision.  */
      for (i = 10; i <= real_info->radix; i *= 10)
	if (i == real_info->radix)
	  real_info->precision++;

      mpfr_clear (a);
      mpfr_clear (b);
      mpfr_clear (c);
    }

  mpz_clear (r);
}


/* Clean up, get rid of numeric constants.  */

void
gfc_arith_done_1 (void)
{
  gfc_integer_info *ip;
  gfc_real_info *rp;

  for (ip = gfc_integer_kinds; ip->kind; ip++)
    {
      mpz_clear (ip->min_int);
      mpz_clear (ip->pedantic_min_int);
      mpz_clear (ip->huge);
    }

  for (rp = gfc_real_kinds; rp->kind; rp++)
    {
      mpfr_clear (rp->epsilon);
      mpfr_clear (rp->huge);
      mpfr_clear (rp->tiny);
      mpfr_clear (rp->subnormal);
    }
}


/* Given an integer and a kind, make sure that the integer lies within
   the range of the kind.  Returns ARITH_OK, ARITH_ASYMMETRIC or
   ARITH_OVERFLOW.  */

arith
gfc_check_integer_range (mpz_t p, int kind)
{
  arith result;
  int i;

  i = gfc_validate_kind (BT_INTEGER, kind, false);
  result = ARITH_OK;

  if (pedantic)
    {
      if (mpz_cmp (p, gfc_integer_kinds[i].pedantic_min_int) < 0)
        result = ARITH_ASYMMETRIC;
    }


  if (gfc_option.flag_range_check == 0)
    return result;

  if (mpz_cmp (p, gfc_integer_kinds[i].min_int) < 0
      || mpz_cmp (p, gfc_integer_kinds[i].huge) > 0)
    result = ARITH_OVERFLOW;

  return result;
}


/* Given a real and a kind, make sure that the real lies within the
   range of the kind.  Returns ARITH_OK, ARITH_OVERFLOW or
   ARITH_UNDERFLOW.  */

static arith
gfc_check_real_range (mpfr_t p, int kind)
{
  arith retval;
  mpfr_t q;
  int i;

  i = gfc_validate_kind (BT_REAL, kind, false);

  gfc_set_model (p);
  mpfr_init (q);
  mpfr_abs (q, p, GFC_RND_MODE);

  if (mpfr_inf_p (p))
    {
      if (gfc_option.flag_range_check == 0)
        retval = ARITH_OK;
      else
        retval = ARITH_OVERFLOW;
    }
  else if (mpfr_nan_p (p))
    {
      if (gfc_option.flag_range_check == 0)
        retval = ARITH_OK;
      else
        retval = ARITH_NAN;
    }
  else if (mpfr_sgn (q) == 0)
    retval = ARITH_OK;
  else if (mpfr_cmp (q, gfc_real_kinds[i].huge) > 0)
    {
      if (gfc_option.flag_range_check == 0)
        retval = ARITH_OK;
      else
        retval = ARITH_OVERFLOW;
    }
  else if (mpfr_cmp (q, gfc_real_kinds[i].subnormal) < 0)
    {
      if (gfc_option.flag_range_check == 0)
        retval = ARITH_OK;
      else
        retval = ARITH_UNDERFLOW;
    }
  else if (mpfr_cmp (q, gfc_real_kinds[i].tiny) < 0)
    {
#if MPFR_VERSION_MAJOR < 2 || (MPFR_VERSION_MAJOR == 2 && MPFR_VERSION_MINOR < 2)
      /* MPFR operates on a number with a given precision and enormous
	exponential range.  To represent subnormal numbers, the exponent is
	allowed to become smaller than emin, but always retains the full
	precision.  This code resets unused bits to 0 to alleviate
	rounding problems.  Note, a future version of MPFR will have a
 	mpfr_subnormalize() function, which handles this truncation in a
	more efficient and robust way.  */

      int j, k;
      char *bin, *s;
      mp_exp_t e;

      bin = mpfr_get_str (NULL, &e, gfc_real_kinds[i].radix, 0, q, GMP_RNDN);
      k = gfc_real_kinds[i].digits - (gfc_real_kinds[i].min_exponent - e);
      for (j = k; j < gfc_real_kinds[i].digits; j++)
	bin[j] = '0';
      /* Need space for '0.', bin, 'E', and e */
      s = (char *) gfc_getmem (strlen(bin) + 10);
      sprintf (s, "0.%sE%d", bin, (int) e);
      mpfr_set_str (q, s, gfc_real_kinds[i].radix, GMP_RNDN);

      gfc_free (s);
      gfc_free (bin);
#else
      mp_exp_t emin, emax;

      /* Save current values of emin and emax.  */
      emin = mpfr_get_emin ();
      emax = mpfr_get_emax ();

      /* Set emin and emax for the current model number.  */
      mpfr_set_emin ((mp_exp_t) gfc_real_kinds[i].min_exponent - 1);
      mpfr_set_emax ((mp_exp_t) gfc_real_kinds[i].max_exponent - 1);
      mpfr_subnormalize (q, 0, GFC_RND_MODE);

      /* Reset emin and emax.  */
      mpfr_set_emin (emin);
      mpfr_set_emax (emax);
#endif

      /* Copy sign if needed.  */
      if (mpfr_sgn (p) < 0)
	mpfr_neg (p, q, GMP_RNDN);
      else
	mpfr_set (p, q, GMP_RNDN);

      retval = ARITH_OK;
    }
  else
    retval = ARITH_OK;

  mpfr_clear (q);

  return retval;
}


/* Function to return a constant expression node of a given type and kind.  */

gfc_expr *
gfc_constant_result (bt type, int kind, locus * where)
{
  gfc_expr *result;

  if (!where)
    gfc_internal_error
      ("gfc_constant_result(): locus 'where' cannot be NULL");

  result = gfc_get_expr ();

  result->expr_type = EXPR_CONSTANT;
  result->ts.type = type;
  result->ts.kind = kind;
  result->where = *where;

  switch (type)
    {
    case BT_INTEGER:
      mpz_init (result->value.integer);
      break;

    case BT_REAL:
      gfc_set_model_kind (kind);
      mpfr_init (result->value.real);
      break;

    case BT_COMPLEX:
      gfc_set_model_kind (kind);
      mpfr_init (result->value.complex.r);
      mpfr_init (result->value.complex.i);
      break;

    default:
      break;
    }

  return result;
}


/* Low-level arithmetic functions.  All of these subroutines assume
   that all operands are of the same type and return an operand of the
   same type.  The other thing about these subroutines is that they
   can fail in various ways -- overflow, underflow, division by zero,
   zero raised to the zero, etc.  */

static arith
gfc_arith_not (gfc_expr * op1, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, op1->ts.kind, &op1->where);
  result->value.logical = !op1->value.logical;
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_and (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_kind_max (op1, op2),
				&op1->where);
  result->value.logical = op1->value.logical && op2->value.logical;
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_or (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_kind_max (op1, op2),
				&op1->where);
  result->value.logical = op1->value.logical || op2->value.logical;
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_eqv (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_kind_max (op1, op2),
				&op1->where);
  result->value.logical = op1->value.logical == op2->value.logical;
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_neqv (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_kind_max (op1, op2),
				&op1->where);
  result->value.logical = op1->value.logical != op2->value.logical;
  *resultp = result;

  return ARITH_OK;
}


/* Make sure a constant numeric expression is within the range for
   its type and kind.  Note that there's also a gfc_check_range(),
   but that one deals with the intrinsic RANGE function.  */

arith
gfc_range_check (gfc_expr * e)
{
  arith rc;

  switch (e->ts.type)
    {
    case BT_INTEGER:
      rc = gfc_check_integer_range (e->value.integer, e->ts.kind);
      break;

    case BT_REAL:
      rc = gfc_check_real_range (e->value.real, e->ts.kind);
      if (rc == ARITH_UNDERFLOW)
	mpfr_set_ui (e->value.real, 0, GFC_RND_MODE);
      if (rc == ARITH_OVERFLOW)
	mpfr_set_inf (e->value.real, mpfr_sgn (e->value.real));
      if (rc == ARITH_NAN)
	mpfr_set_nan (e->value.real);
      break;

    case BT_COMPLEX:
      rc = gfc_check_real_range (e->value.complex.r, e->ts.kind);
      if (rc == ARITH_UNDERFLOW)
	mpfr_set_ui (e->value.complex.r, 0, GFC_RND_MODE);
      if (rc == ARITH_OVERFLOW)
	mpfr_set_inf (e->value.complex.r, mpfr_sgn (e->value.complex.r));
      if (rc == ARITH_NAN)
	mpfr_set_nan (e->value.complex.r);

      rc = gfc_check_real_range (e->value.complex.i, e->ts.kind);
      if (rc == ARITH_UNDERFLOW)
	mpfr_set_ui (e->value.complex.i, 0, GFC_RND_MODE);
      if (rc == ARITH_OVERFLOW)
	mpfr_set_inf (e->value.complex.i, mpfr_sgn (e->value.complex.i));
      if (rc == ARITH_NAN)
	mpfr_set_nan (e->value.complex.i);
      break;

    default:
      gfc_internal_error ("gfc_range_check(): Bad type");
    }

  return rc;
}


/* Several of the following routines use the same set of statements to
   check the validity of the result.  Encapsulate the checking here.  */

static arith
check_result (arith rc, gfc_expr * x, gfc_expr * r, gfc_expr ** rp)
{
  arith val = rc;

  if (val == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
	gfc_warning (gfc_arith_error (val), &x->where);
      val = ARITH_OK;
    }

  if (val == ARITH_ASYMMETRIC)
    {
      gfc_warning (gfc_arith_error (val), &x->where);
      val = ARITH_OK;
    }

  if (val != ARITH_OK)
    gfc_free_expr (r);
  else
    *rp = r;

  return val;
}


/* It may seem silly to have a subroutine that actually computes the
   unary plus of a constant, but it prevents us from making exceptions
   in the code elsewhere.  */

static arith
gfc_arith_uplus (gfc_expr * op1, gfc_expr ** resultp)
{
  *resultp = gfc_copy_expr (op1);
  return ARITH_OK;
}


static arith
gfc_arith_uminus (gfc_expr * op1, gfc_expr ** resultp)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      mpz_neg (result->value.integer, op1->value.integer);
      break;

    case BT_REAL:
      mpfr_neg (result->value.real, op1->value.real, GFC_RND_MODE);
      break;

    case BT_COMPLEX:
      mpfr_neg (result->value.complex.r, op1->value.complex.r, GFC_RND_MODE);
      mpfr_neg (result->value.complex.i, op1->value.complex.i, GFC_RND_MODE);
      break;

    default:
      gfc_internal_error ("gfc_arith_uminus(): Bad basic type");
    }

  rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


static arith
gfc_arith_plus (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      mpz_add (result->value.integer, op1->value.integer, op2->value.integer);
      break;

    case BT_REAL:
      mpfr_add (result->value.real, op1->value.real, op2->value.real,
               GFC_RND_MODE);
      break;

    case BT_COMPLEX:
      mpfr_add (result->value.complex.r, op1->value.complex.r,
	       op2->value.complex.r, GFC_RND_MODE);

      mpfr_add (result->value.complex.i, op1->value.complex.i,
	       op2->value.complex.i, GFC_RND_MODE);
      break;

    default:
      gfc_internal_error ("gfc_arith_plus(): Bad basic type");
    }

  rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


static arith
gfc_arith_minus (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      mpz_sub (result->value.integer, op1->value.integer, op2->value.integer);
      break;

    case BT_REAL:
      mpfr_sub (result->value.real, op1->value.real, op2->value.real,
                GFC_RND_MODE);
      break;

    case BT_COMPLEX:
      mpfr_sub (result->value.complex.r, op1->value.complex.r,
	       op2->value.complex.r, GFC_RND_MODE);

      mpfr_sub (result->value.complex.i, op1->value.complex.i,
	       op2->value.complex.i, GFC_RND_MODE);
      break;

    default:
      gfc_internal_error ("gfc_arith_minus(): Bad basic type");
    }

  rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


static arith
gfc_arith_times (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;
  mpfr_t x, y;
  arith rc;

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      mpz_mul (result->value.integer, op1->value.integer, op2->value.integer);
      break;

    case BT_REAL:
      mpfr_mul (result->value.real, op1->value.real, op2->value.real,
               GFC_RND_MODE);
      break;

    case BT_COMPLEX:
      gfc_set_model (op1->value.complex.r);
      mpfr_init (x);
      mpfr_init (y);

      mpfr_mul (x, op1->value.complex.r, op2->value.complex.r, GFC_RND_MODE);
      mpfr_mul (y, op1->value.complex.i, op2->value.complex.i, GFC_RND_MODE);
      mpfr_sub (result->value.complex.r, x, y, GFC_RND_MODE);

      mpfr_mul (x, op1->value.complex.r, op2->value.complex.i, GFC_RND_MODE);
      mpfr_mul (y, op1->value.complex.i, op2->value.complex.r, GFC_RND_MODE);
      mpfr_add (result->value.complex.i, x, y, GFC_RND_MODE);

      mpfr_clear (x);
      mpfr_clear (y);
      break;

    default:
      gfc_internal_error ("gfc_arith_times(): Bad basic type");
    }

  rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


static arith
gfc_arith_divide (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;
  mpfr_t x, y, div;
  arith rc;

  rc = ARITH_OK;

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      if (mpz_sgn (op2->value.integer) == 0)
	{
	  rc = ARITH_DIV0;
	  break;
	}

      mpz_tdiv_q (result->value.integer, op1->value.integer,
		  op2->value.integer);
      break;

    case BT_REAL:
      if (mpfr_sgn (op2->value.real) == 0
	  && gfc_option.flag_range_check == 1)
	{
	  rc = ARITH_DIV0;
	  break;
	}

      mpfr_div (result->value.real, op1->value.real, op2->value.real,
               GFC_RND_MODE);
      break;

    case BT_COMPLEX:
      if (mpfr_sgn (op2->value.complex.r) == 0
	  && mpfr_sgn (op2->value.complex.i) == 0
	  && gfc_option.flag_range_check == 1)
	{
	  rc = ARITH_DIV0;
	  break;
	}

      gfc_set_model (op1->value.complex.r);
      mpfr_init (x);
      mpfr_init (y);
      mpfr_init (div);

      mpfr_mul (x, op2->value.complex.r, op2->value.complex.r, GFC_RND_MODE);
      mpfr_mul (y, op2->value.complex.i, op2->value.complex.i, GFC_RND_MODE);
      mpfr_add (div, x, y, GFC_RND_MODE);

      mpfr_mul (x, op1->value.complex.r, op2->value.complex.r, GFC_RND_MODE);
      mpfr_mul (y, op1->value.complex.i, op2->value.complex.i, GFC_RND_MODE);
      mpfr_add (result->value.complex.r, x, y, GFC_RND_MODE);
      mpfr_div (result->value.complex.r, result->value.complex.r, div,
                GFC_RND_MODE);

      mpfr_mul (x, op1->value.complex.i, op2->value.complex.r, GFC_RND_MODE);
      mpfr_mul (y, op1->value.complex.r, op2->value.complex.i, GFC_RND_MODE);
      mpfr_sub (result->value.complex.i, x, y, GFC_RND_MODE);
      mpfr_div (result->value.complex.i, result->value.complex.i, div,
                GFC_RND_MODE);

      mpfr_clear (x);
      mpfr_clear (y);
      mpfr_clear (div);
      break;

    default:
      gfc_internal_error ("gfc_arith_divide(): Bad basic type");
    }

  if (rc == ARITH_OK)
    rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


/* Compute the reciprocal of a complex number (guaranteed nonzero).  */

static void
complex_reciprocal (gfc_expr * op)
{
  mpfr_t mod, a, re, im;

  gfc_set_model (op->value.complex.r);
  mpfr_init (mod);
  mpfr_init (a);
  mpfr_init (re);
  mpfr_init (im);

  mpfr_mul (mod, op->value.complex.r, op->value.complex.r, GFC_RND_MODE);
  mpfr_mul (a, op->value.complex.i, op->value.complex.i, GFC_RND_MODE);
  mpfr_add (mod, mod, a, GFC_RND_MODE);

  mpfr_div (re, op->value.complex.r, mod, GFC_RND_MODE);

  mpfr_neg (im, op->value.complex.i, GFC_RND_MODE);
  mpfr_div (im, im, mod, GFC_RND_MODE);

  mpfr_set (op->value.complex.r, re, GFC_RND_MODE);
  mpfr_set (op->value.complex.i, im, GFC_RND_MODE);

  mpfr_clear (re);
  mpfr_clear (im);
  mpfr_clear (mod);
  mpfr_clear (a);
}


/* Raise a complex number to positive power.  */

static void
complex_pow_ui (gfc_expr * base, int power, gfc_expr * result)
{
  mpfr_t re, im, a;

  gfc_set_model (base->value.complex.r);
  mpfr_init (re);
  mpfr_init (im);
  mpfr_init (a);

  mpfr_set_ui (result->value.complex.r, 1, GFC_RND_MODE);
  mpfr_set_ui (result->value.complex.i, 0, GFC_RND_MODE);

  for (; power > 0; power--)
    {
      mpfr_mul (re, base->value.complex.r, result->value.complex.r,
                GFC_RND_MODE);
      mpfr_mul (a, base->value.complex.i, result->value.complex.i,
                GFC_RND_MODE);
      mpfr_sub (re, re, a, GFC_RND_MODE);

      mpfr_mul (im, base->value.complex.r, result->value.complex.i,
                GFC_RND_MODE);
      mpfr_mul (a, base->value.complex.i, result->value.complex.r,
                GFC_RND_MODE);
      mpfr_add (im, im, a, GFC_RND_MODE);

      mpfr_set (result->value.complex.r, re, GFC_RND_MODE);
      mpfr_set (result->value.complex.i, im, GFC_RND_MODE);
    }

  mpfr_clear (re);
  mpfr_clear (im);
  mpfr_clear (a);
}


/* Raise a number to an integer power.  */

static arith
gfc_arith_power (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  int power, apower;
  gfc_expr *result;
  mpz_t unity_z;
  mpfr_t unity_f;
  arith rc;

  rc = ARITH_OK;

  if (gfc_extract_int (op2, &power) != NULL)
    gfc_internal_error ("gfc_arith_power(): Bad exponent");

  result = gfc_constant_result (op1->ts.type, op1->ts.kind, &op1->where);

  if (power == 0)
    {
      /* Handle something to the zeroth power.  Since we're dealing
	 with integral exponents, there is no ambiguity in the
	 limiting procedure used to determine the value of 0**0.  */
      switch (op1->ts.type)
	{
	case BT_INTEGER:
	  mpz_set_ui (result->value.integer, 1);
	  break;

	case BT_REAL:
	  mpfr_set_ui (result->value.real, 1, GFC_RND_MODE);
	  break;

	case BT_COMPLEX:
	  mpfr_set_ui (result->value.complex.r, 1, GFC_RND_MODE);
	  mpfr_set_ui (result->value.complex.i, 0, GFC_RND_MODE);
	  break;

	default:
	  gfc_internal_error ("gfc_arith_power(): Bad base");
	}
    }
  else
    {
      apower = power;
      if (power < 0)
	apower = -power;

      switch (op1->ts.type)
	{
	case BT_INTEGER:
	  mpz_pow_ui (result->value.integer, op1->value.integer, apower);

	  if (power < 0)
	    {
	      mpz_init_set_ui (unity_z, 1);
	      mpz_tdiv_q (result->value.integer, unity_z,
			  result->value.integer);
	      mpz_clear (unity_z);
	    }
	  break;

	case BT_REAL:
	  mpfr_pow_ui (result->value.real, op1->value.real, apower,
                       GFC_RND_MODE);

	  if (power < 0)
	    {
              gfc_set_model (op1->value.real);
	      mpfr_init (unity_f);
	      mpfr_set_ui (unity_f, 1, GFC_RND_MODE);
	      mpfr_div (result->value.real, unity_f, result->value.real,
                        GFC_RND_MODE);
	      mpfr_clear (unity_f);
	    }
	  break;

	case BT_COMPLEX:
	  complex_pow_ui (op1, apower, result);
	  if (power < 0)
	    complex_reciprocal (result);
	  break;

	default:
	  break;
	}
    }

  if (rc == ARITH_OK)
    rc = gfc_range_check (result);

  return check_result (rc, op1, result, resultp);
}


/* Concatenate two string constants.  */

static arith
gfc_arith_concat (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;
  int len;

  result = gfc_constant_result (BT_CHARACTER, gfc_default_character_kind,
				&op1->where);

  len = op1->value.character.length + op2->value.character.length;

  result->value.character.string = gfc_getmem (len + 1);
  result->value.character.length = len;

  memcpy (result->value.character.string, op1->value.character.string,
	  op1->value.character.length);

  memcpy (result->value.character.string + op1->value.character.length,
	  op2->value.character.string, op2->value.character.length);

  result->value.character.string[len] = '\0';

  *resultp = result;

  return ARITH_OK;
}


/* Comparison operators.  Assumes that the two expression nodes
   contain two constants of the same type.  */

int
gfc_compare_expr (gfc_expr * op1, gfc_expr * op2)
{
  int rc;

  switch (op1->ts.type)
    {
    case BT_INTEGER:
      rc = mpz_cmp (op1->value.integer, op2->value.integer);
      break;

    case BT_REAL:
      rc = mpfr_cmp (op1->value.real, op2->value.real);
      break;

    case BT_CHARACTER:
      rc = gfc_compare_string (op1, op2, NULL);
      break;

    case BT_LOGICAL:
      rc = ((!op1->value.logical && op2->value.logical)
	    || (op1->value.logical && !op2->value.logical));
      break;

    default:
      gfc_internal_error ("gfc_compare_expr(): Bad basic type");
    }

  return rc;
}


/* Compare a pair of complex numbers.  Naturally, this is only for
   equality and nonequality.  */

static int
compare_complex (gfc_expr * op1, gfc_expr * op2)
{
  return (mpfr_cmp (op1->value.complex.r, op2->value.complex.r) == 0
	  && mpfr_cmp (op1->value.complex.i, op2->value.complex.i) == 0);
}


/* Given two constant strings and the inverse collating sequence, compare the
   strings.  We return -1 for a < b, 0 for a == b and 1 for a > b.  If the
   xcoll_table is NULL, we use the processor's default collating sequence.  */

int
gfc_compare_string (gfc_expr * a, gfc_expr * b, const int * xcoll_table)
{
  int len, alen, blen, i, ac, bc;

  alen = a->value.character.length;
  blen = b->value.character.length;

  len = (alen > blen) ? alen : blen;

  for (i = 0; i < len; i++)
    {
      /* We cast to unsigned char because default char, if it is signed,
         would lead to ac < 0 for string[i] > 127.  */
      ac = (unsigned char) ((i < alen) ? a->value.character.string[i] : ' ');
      bc = (unsigned char) ((i < blen) ? b->value.character.string[i] : ' ');

      if (xcoll_table != NULL)
	{
	  ac = xcoll_table[ac];
	  bc = xcoll_table[bc];
	}

      if (ac < bc)
	return -1;
      if (ac > bc)
	return 1;
    }

  /* Strings are equal */

  return 0;
}


/* Specific comparison subroutines.  */

static arith
gfc_arith_eq (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (op1->ts.type == BT_COMPLEX) ?
    compare_complex (op1, op2) : (gfc_compare_expr (op1, op2) == 0);

  *resultp = result;
  return ARITH_OK;
}


static arith
gfc_arith_ne (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (op1->ts.type == BT_COMPLEX) ?
    !compare_complex (op1, op2) : (gfc_compare_expr (op1, op2) != 0);

  *resultp = result;
  return ARITH_OK;
}


static arith
gfc_arith_gt (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (gfc_compare_expr (op1, op2) > 0);
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_ge (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (gfc_compare_expr (op1, op2) >= 0);
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_lt (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (gfc_compare_expr (op1, op2) < 0);
  *resultp = result;

  return ARITH_OK;
}


static arith
gfc_arith_le (gfc_expr * op1, gfc_expr * op2, gfc_expr ** resultp)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, gfc_default_logical_kind,
				&op1->where);
  result->value.logical = (gfc_compare_expr (op1, op2) <= 0);
  *resultp = result;

  return ARITH_OK;
}


static arith
reduce_unary (arith (*eval) (gfc_expr *, gfc_expr **), gfc_expr * op,
	      gfc_expr ** result)
{
  gfc_constructor *c, *head;
  gfc_expr *r;
  arith rc;

  if (op->expr_type == EXPR_CONSTANT)
    return eval (op, result);

  rc = ARITH_OK;
  head = gfc_copy_constructor (op->value.constructor);

  for (c = head; c; c = c->next)
    {
      rc = eval (c->expr, &r);
      if (rc != ARITH_OK)
	break;

      gfc_replace_expr (c->expr, r);
    }

  if (rc != ARITH_OK)
    gfc_free_constructor (head);
  else
    {
      r = gfc_get_expr ();
      r->expr_type = EXPR_ARRAY;
      r->value.constructor = head;
      r->shape = gfc_copy_shape (op->shape, op->rank);

      r->ts = head->expr->ts;
      r->where = op->where;
      r->rank = op->rank;

      *result = r;
    }

  return rc;
}


static arith
reduce_binary_ac (arith (*eval) (gfc_expr *, gfc_expr *, gfc_expr **),
		  gfc_expr * op1, gfc_expr * op2,
		  gfc_expr ** result)
{
  gfc_constructor *c, *head;
  gfc_expr *r;
  arith rc;

  head = gfc_copy_constructor (op1->value.constructor);
  rc = ARITH_OK;

  for (c = head; c; c = c->next)
    {
      rc = eval (c->expr, op2, &r);
      if (rc != ARITH_OK)
	break;

      gfc_replace_expr (c->expr, r);
    }

  if (rc != ARITH_OK)
    gfc_free_constructor (head);
  else
    {
      r = gfc_get_expr ();
      r->expr_type = EXPR_ARRAY;
      r->value.constructor = head;
      r->shape = gfc_copy_shape (op1->shape, op1->rank);

      r->ts = head->expr->ts;
      r->where = op1->where;
      r->rank = op1->rank;

      *result = r;
    }

  return rc;
}


static arith
reduce_binary_ca (arith (*eval) (gfc_expr *, gfc_expr *, gfc_expr **),
		  gfc_expr * op1, gfc_expr * op2,
		  gfc_expr ** result)
{
  gfc_constructor *c, *head;
  gfc_expr *r;
  arith rc;

  head = gfc_copy_constructor (op2->value.constructor);
  rc = ARITH_OK;

  for (c = head; c; c = c->next)
    {
      rc = eval (op1, c->expr, &r);
      if (rc != ARITH_OK)
	break;

      gfc_replace_expr (c->expr, r);
    }

  if (rc != ARITH_OK)
    gfc_free_constructor (head);
  else
    {
      r = gfc_get_expr ();
      r->expr_type = EXPR_ARRAY;
      r->value.constructor = head;
      r->shape = gfc_copy_shape (op2->shape, op2->rank);

      r->ts = head->expr->ts;
      r->where = op2->where;
      r->rank = op2->rank;

      *result = r;
    }

  return rc;
}


static arith
reduce_binary_aa (arith (*eval) (gfc_expr *, gfc_expr *, gfc_expr **),
		  gfc_expr * op1, gfc_expr * op2,
		  gfc_expr ** result)
{
  gfc_constructor *c, *d, *head;
  gfc_expr *r;
  arith rc;

  head = gfc_copy_constructor (op1->value.constructor);

  rc = ARITH_OK;
  d = op2->value.constructor;

  if (gfc_check_conformance ("Elemental binary operation", op1, op2)
      != SUCCESS)
    rc = ARITH_INCOMMENSURATE;
  else
    {

      for (c = head; c; c = c->next, d = d->next)
	{
	  if (d == NULL)
	    {
	      rc = ARITH_INCOMMENSURATE;
	      break;
	    }

	  rc = eval (c->expr, d->expr, &r);
	  if (rc != ARITH_OK)
	    break;

	  gfc_replace_expr (c->expr, r);
	}

      if (d != NULL)
	rc = ARITH_INCOMMENSURATE;
    }

  if (rc != ARITH_OK)
    gfc_free_constructor (head);
  else
    {
      r = gfc_get_expr ();
      r->expr_type = EXPR_ARRAY;
      r->value.constructor = head;
      r->shape = gfc_copy_shape (op1->shape, op1->rank);

      r->ts = head->expr->ts;
      r->where = op1->where;
      r->rank = op1->rank;

      *result = r;
    }

  return rc;
}


static arith
reduce_binary (arith (*eval) (gfc_expr *, gfc_expr *, gfc_expr **),
	       gfc_expr * op1, gfc_expr * op2,
	       gfc_expr ** result)
{
  if (op1->expr_type == EXPR_CONSTANT && op2->expr_type == EXPR_CONSTANT)
    return eval (op1, op2, result);

  if (op1->expr_type == EXPR_CONSTANT && op2->expr_type == EXPR_ARRAY)
    return reduce_binary_ca (eval, op1, op2, result);

  if (op1->expr_type == EXPR_ARRAY && op2->expr_type == EXPR_CONSTANT)
    return reduce_binary_ac (eval, op1, op2, result);

  return reduce_binary_aa (eval, op1, op2, result);
}


typedef union
{
  arith (*f2)(gfc_expr *, gfc_expr **);
  arith (*f3)(gfc_expr *, gfc_expr *, gfc_expr **);
}
eval_f;

/* High level arithmetic subroutines.  These subroutines go into
   eval_intrinsic(), which can do one of several things to its
   operands.  If the operands are incompatible with the intrinsic
   operation, we return a node pointing to the operands and hope that
   an operator interface is found during resolution.

   If the operands are compatible and are constants, then we try doing
   the arithmetic.  We also handle the cases where either or both
   operands are array constructors.  */

static gfc_expr *
eval_intrinsic (gfc_intrinsic_op operator,
		eval_f eval, gfc_expr * op1, gfc_expr * op2)
{
  gfc_expr temp, *result;
  int unary;
  arith rc;

  gfc_clear_ts (&temp.ts);

  switch (operator)
    {
    /* Logical unary  */
    case INTRINSIC_NOT:
      if (op1->ts.type != BT_LOGICAL)
	goto runtime;

      temp.ts.type = BT_LOGICAL;
      temp.ts.kind = gfc_default_logical_kind;

      unary = 1;
      break;

    /* Logical binary operators  */
    case INTRINSIC_OR:
    case INTRINSIC_AND:
    case INTRINSIC_NEQV:
    case INTRINSIC_EQV:
      if (op1->ts.type != BT_LOGICAL || op2->ts.type != BT_LOGICAL)
	goto runtime;

      temp.ts.type = BT_LOGICAL;
      temp.ts.kind = gfc_default_logical_kind;

      unary = 0;
      break;

    /* Numeric unary  */
    case INTRINSIC_UPLUS:
    case INTRINSIC_UMINUS:
      if (!gfc_numeric_ts (&op1->ts))
	goto runtime;

      temp.ts = op1->ts;

      unary = 1;
      break;

    case INTRINSIC_PARENTHESES:
      temp.ts = op1->ts;

      unary = 1;
      break;

    /* Additional restrictions for ordering relations.  */
    case INTRINSIC_GE:
    case INTRINSIC_LT:
    case INTRINSIC_LE:
    case INTRINSIC_GT:
      if (op1->ts.type == BT_COMPLEX || op2->ts.type == BT_COMPLEX)
	{
	  temp.ts.type = BT_LOGICAL;
	  temp.ts.kind = gfc_default_logical_kind;
	  goto runtime;
	}

    /* Fall through  */
    case INTRINSIC_EQ:
    case INTRINSIC_NE:
      if (op1->ts.type == BT_CHARACTER && op2->ts.type == BT_CHARACTER)
	{
	  unary = 0;
	  temp.ts.type = BT_LOGICAL;
	  temp.ts.kind = gfc_default_logical_kind;
	  break;
	}

    /* Fall through  */
    /* Numeric binary  */
    case INTRINSIC_PLUS:
    case INTRINSIC_MINUS:
    case INTRINSIC_TIMES:
    case INTRINSIC_DIVIDE:
    case INTRINSIC_POWER:
      if (!gfc_numeric_ts (&op1->ts) || !gfc_numeric_ts (&op2->ts))
	goto runtime;

      /* Insert any necessary type conversions to make the operands
	 compatible.  */

      temp.expr_type = EXPR_OP;
      gfc_clear_ts (&temp.ts);
      temp.value.op.operator = operator;

      temp.value.op.op1 = op1;
      temp.value.op.op2 = op2;

      gfc_type_convert_binary (&temp);

      if (operator == INTRINSIC_EQ || operator == INTRINSIC_NE
	  || operator == INTRINSIC_GE || operator == INTRINSIC_GT
	  || operator == INTRINSIC_LE || operator == INTRINSIC_LT)
	{
	  temp.ts.type = BT_LOGICAL;
	  temp.ts.kind = gfc_default_logical_kind;
	}

      unary = 0;
      break;

    /* Character binary  */
    case INTRINSIC_CONCAT:
      if (op1->ts.type != BT_CHARACTER || op2->ts.type != BT_CHARACTER)
	goto runtime;

      temp.ts.type = BT_CHARACTER;
      temp.ts.kind = gfc_default_character_kind;

      unary = 0;
      break;

    case INTRINSIC_USER:
      goto runtime;

    default:
      gfc_internal_error ("eval_intrinsic(): Bad operator");
    }

  /* Try to combine the operators.  */
  if (operator == INTRINSIC_POWER && op2->ts.type != BT_INTEGER)
    goto runtime;

  if (op1->from_H
      || (op1->expr_type != EXPR_CONSTANT
	  && (op1->expr_type != EXPR_ARRAY
	      || !gfc_is_constant_expr (op1)
	      || !gfc_expanded_ac (op1))))
    goto runtime;

  if (op2 != NULL
      && (op2->from_H
	  || (op2->expr_type != EXPR_CONSTANT
	      && (op2->expr_type != EXPR_ARRAY
	      || !gfc_is_constant_expr (op2)
	      || !gfc_expanded_ac (op2)))))
    goto runtime;

  if (unary)
    rc = reduce_unary (eval.f2, op1, &result);
  else
    rc = reduce_binary (eval.f3, op1, op2, &result);

  if (rc != ARITH_OK)
    { /* Something went wrong.  */
      gfc_error (gfc_arith_error (rc), &op1->where);
      return NULL;
    }

  gfc_free_expr (op1);
  gfc_free_expr (op2);
  return result;

runtime:
  /* Create a run-time expression.  */
  result = gfc_get_expr ();
  result->ts = temp.ts;

  result->expr_type = EXPR_OP;
  result->value.op.operator = operator;

  result->value.op.op1 = op1;
  result->value.op.op2 = op2;

  result->where = op1->where;

  return result;
}


/* Modify type of expression for zero size array.  */

static gfc_expr *
eval_type_intrinsic0 (gfc_intrinsic_op operator, gfc_expr * op)
{
  if (op == NULL)
    gfc_internal_error ("eval_type_intrinsic0(): op NULL");

  switch (operator)
    {
    case INTRINSIC_GE:
    case INTRINSIC_LT:
    case INTRINSIC_LE:
    case INTRINSIC_GT:
    case INTRINSIC_EQ:
    case INTRINSIC_NE:
      op->ts.type = BT_LOGICAL;
      op->ts.kind = gfc_default_logical_kind;
      break;

    default:
      break;
    }

  return op;
}


/* Return nonzero if the expression is a zero size array.  */

static int
gfc_zero_size_array (gfc_expr * e)
{
  if (e->expr_type != EXPR_ARRAY)
    return 0;

  return e->value.constructor == NULL;
}


/* Reduce a binary expression where at least one of the operands
   involves a zero-length array.  Returns NULL if neither of the
   operands is a zero-length array.  */

static gfc_expr *
reduce_binary0 (gfc_expr * op1, gfc_expr * op2)
{
  if (gfc_zero_size_array (op1))
    {
      gfc_free_expr (op2);
      return op1;
    }

  if (gfc_zero_size_array (op2))
    {
      gfc_free_expr (op1);
      return op2;
    }

  return NULL;
}


static gfc_expr *
eval_intrinsic_f2 (gfc_intrinsic_op operator,
		   arith (*eval) (gfc_expr *, gfc_expr **),
		   gfc_expr * op1, gfc_expr * op2)
{
  gfc_expr *result;
  eval_f f;

  if (op2 == NULL)
    {
      if (gfc_zero_size_array (op1))
	return eval_type_intrinsic0 (operator, op1);
    }
  else
    {
      result = reduce_binary0 (op1, op2);
      if (result != NULL)
	return eval_type_intrinsic0 (operator, result);
    }

  f.f2 = eval;
  return eval_intrinsic (operator, f, op1, op2);
}


static gfc_expr *
eval_intrinsic_f3 (gfc_intrinsic_op operator,
		   arith (*eval) (gfc_expr *, gfc_expr *, gfc_expr **),
		   gfc_expr * op1, gfc_expr * op2)
{
  gfc_expr *result;
  eval_f f;

  result = reduce_binary0 (op1, op2);
  if (result != NULL)
    return eval_type_intrinsic0(operator, result);

  f.f3 = eval;
  return eval_intrinsic (operator, f, op1, op2);
}


gfc_expr *
gfc_uplus (gfc_expr * op)
{
  return eval_intrinsic_f2 (INTRINSIC_UPLUS, gfc_arith_uplus, op, NULL);
}


gfc_expr *
gfc_uminus (gfc_expr * op)
{
  return eval_intrinsic_f2 (INTRINSIC_UMINUS, gfc_arith_uminus, op, NULL);
}


gfc_expr *
gfc_add (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_PLUS, gfc_arith_plus, op1, op2);
}


gfc_expr *
gfc_subtract (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_MINUS, gfc_arith_minus, op1, op2);
}


gfc_expr *
gfc_multiply (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_TIMES, gfc_arith_times, op1, op2);
}


gfc_expr *
gfc_divide (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_DIVIDE, gfc_arith_divide, op1, op2);
}


gfc_expr *
gfc_power (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_POWER, gfc_arith_power, op1, op2);
}


gfc_expr *
gfc_concat (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_CONCAT, gfc_arith_concat, op1, op2);
}


gfc_expr *
gfc_and (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_AND, gfc_arith_and, op1, op2);
}


gfc_expr *
gfc_or (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_OR, gfc_arith_or, op1, op2);
}


gfc_expr *
gfc_not (gfc_expr * op1)
{
  return eval_intrinsic_f2 (INTRINSIC_NOT, gfc_arith_not, op1, NULL);
}


gfc_expr *
gfc_eqv (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_EQV, gfc_arith_eqv, op1, op2);
}


gfc_expr *
gfc_neqv (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_NEQV, gfc_arith_neqv, op1, op2);
}


gfc_expr *
gfc_eq (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_EQ, gfc_arith_eq, op1, op2);
}


gfc_expr *
gfc_ne (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_NE, gfc_arith_ne, op1, op2);
}


gfc_expr *
gfc_gt (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_GT, gfc_arith_gt, op1, op2);
}


gfc_expr *
gfc_ge (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_GE, gfc_arith_ge, op1, op2);
}


gfc_expr *
gfc_lt (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_LT, gfc_arith_lt, op1, op2);
}


gfc_expr *
gfc_le (gfc_expr * op1, gfc_expr * op2)
{
  return eval_intrinsic_f3 (INTRINSIC_LE, gfc_arith_le, op1, op2);
}


/* Convert an integer string to an expression node.  */

gfc_expr *
gfc_convert_integer (const char * buffer, int kind, int radix, locus * where)
{
  gfc_expr *e;
  const char *t;

  e = gfc_constant_result (BT_INTEGER, kind, where);
  /* A leading plus is allowed, but not by mpz_set_str.  */
  if (buffer[0] == '+')
    t = buffer + 1;
  else
    t = buffer;
  mpz_set_str (e->value.integer, t, radix);

  return e;
}


/* Convert a real string to an expression node.  */

gfc_expr *
gfc_convert_real (const char * buffer, int kind, locus * where)
{
  gfc_expr *e;

  e = gfc_constant_result (BT_REAL, kind, where);
  mpfr_set_str (e->value.real, buffer, 10, GFC_RND_MODE);

  return e;
}


/* Convert a pair of real, constant expression nodes to a single
   complex expression node.  */

gfc_expr *
gfc_convert_complex (gfc_expr * real, gfc_expr * imag, int kind)
{
  gfc_expr *e;

  e = gfc_constant_result (BT_COMPLEX, kind, &real->where);
  mpfr_set (e->value.complex.r, real->value.real, GFC_RND_MODE);
  mpfr_set (e->value.complex.i, imag->value.real, GFC_RND_MODE);

  return e;
}


/******* Simplification of intrinsic functions with constant arguments *****/


/* Deal with an arithmetic error.  */

static void
arith_error (arith rc, gfc_typespec * from, gfc_typespec * to, locus * where)
{
  switch (rc)
    {
    case ARITH_OK:
      gfc_error ("Arithmetic OK converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_OVERFLOW:
      gfc_error ("Arithmetic overflow converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_UNDERFLOW:
      gfc_error ("Arithmetic underflow converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_NAN:
      gfc_error ("Arithmetic NaN converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_DIV0:
      gfc_error ("Division by zero converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_INCOMMENSURATE:
      gfc_error ("Array operands are incommensurate converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    case ARITH_ASYMMETRIC:
      gfc_error ("Integer outside symmetric range implied by Standard Fortran"
	 	 " converting %s to %s at %L",
		 gfc_typename (from), gfc_typename (to), where);
      break;
    default:
      gfc_internal_error ("gfc_arith_error(): Bad error code");
    }

  /* TODO: Do something about the error, ie, throw exception, return
     NaN, etc.  */
}


/* Convert integers to integers.  */

gfc_expr *
gfc_int2int (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_INTEGER, kind, &src->where);

  mpz_set (result->value.integer, src->value.integer);

  if ((rc = gfc_check_integer_range (result->value.integer, kind))
      != ARITH_OK)
    {
      if (rc == ARITH_ASYMMETRIC)
        {
          gfc_warning (gfc_arith_error (rc), &src->where);
        }
      else
        {
          arith_error (rc, &src->ts, &result->ts, &src->where);
          gfc_free_expr (result);
          return NULL;
        }
    }

  return result;
}


/* Convert integers to reals.  */

gfc_expr *
gfc_int2real (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_REAL, kind, &src->where);

  mpfr_set_z (result->value.real, src->value.integer, GFC_RND_MODE);

  if ((rc = gfc_check_real_range (result->value.real, kind)) != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert default integer to default complex.  */

gfc_expr *
gfc_int2complex (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_COMPLEX, kind, &src->where);

  mpfr_set_z (result->value.complex.r, src->value.integer, GFC_RND_MODE);
  mpfr_set_ui (result->value.complex.i, 0, GFC_RND_MODE);

  if ((rc = gfc_check_real_range (result->value.complex.r, kind)) != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert default real to default integer.  */

gfc_expr *
gfc_real2int (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_INTEGER, kind, &src->where);

  gfc_mpfr_to_mpz (result->value.integer, src->value.real);

  if ((rc = gfc_check_integer_range (result->value.integer, kind))
      != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert real to real.  */

gfc_expr *
gfc_real2real (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_REAL, kind, &src->where);

  mpfr_set (result->value.real, src->value.real, GFC_RND_MODE);

  rc = gfc_check_real_range (result->value.real, kind);

  if (rc == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
        gfc_warning (gfc_arith_error (rc), &src->where);
      mpfr_set_ui (result->value.real, 0, GFC_RND_MODE);
    }
  else if (rc != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert real to complex.  */

gfc_expr *
gfc_real2complex (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_COMPLEX, kind, &src->where);

  mpfr_set (result->value.complex.r, src->value.real, GFC_RND_MODE);
  mpfr_set_ui (result->value.complex.i, 0, GFC_RND_MODE);

  rc = gfc_check_real_range (result->value.complex.r, kind);

  if (rc == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
        gfc_warning (gfc_arith_error (rc), &src->where);
      mpfr_set_ui (result->value.complex.r, 0, GFC_RND_MODE);
    }
  else if (rc != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert complex to integer.  */

gfc_expr *
gfc_complex2int (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_INTEGER, kind, &src->where);

  gfc_mpfr_to_mpz (result->value.integer, src->value.complex.r);

  if ((rc = gfc_check_integer_range (result->value.integer, kind))
      != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert complex to real.  */

gfc_expr *
gfc_complex2real (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_REAL, kind, &src->where);

  mpfr_set (result->value.real, src->value.complex.r, GFC_RND_MODE);

  rc = gfc_check_real_range (result->value.real, kind);

  if (rc == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
        gfc_warning (gfc_arith_error (rc), &src->where);
      mpfr_set_ui (result->value.real, 0, GFC_RND_MODE);
    }
  if (rc != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Convert complex to complex.  */

gfc_expr *
gfc_complex2complex (gfc_expr * src, int kind)
{
  gfc_expr *result;
  arith rc;

  result = gfc_constant_result (BT_COMPLEX, kind, &src->where);

  mpfr_set (result->value.complex.r, src->value.complex.r, GFC_RND_MODE);
  mpfr_set (result->value.complex.i, src->value.complex.i, GFC_RND_MODE);

  rc = gfc_check_real_range (result->value.complex.r, kind);

  if (rc == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
        gfc_warning (gfc_arith_error (rc), &src->where);
      mpfr_set_ui (result->value.complex.r, 0, GFC_RND_MODE);
    }
  else if (rc != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  rc = gfc_check_real_range (result->value.complex.i, kind);

  if (rc == ARITH_UNDERFLOW)
    {
      if (gfc_option.warn_underflow)
        gfc_warning (gfc_arith_error (rc), &src->where);
      mpfr_set_ui (result->value.complex.i, 0, GFC_RND_MODE);
    }
  else if (rc != ARITH_OK)
    {
      arith_error (rc, &src->ts, &result->ts, &src->where);
      gfc_free_expr (result);
      return NULL;
    }

  return result;
}


/* Logical kind conversion.  */

gfc_expr *
gfc_log2log (gfc_expr * src, int kind)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, kind, &src->where);
  result->value.logical = src->value.logical;

  return result;
}


/* Convert logical to integer.  */

gfc_expr *
gfc_log2int (gfc_expr *src, int kind)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_INTEGER, kind, &src->where);
  mpz_set_si (result->value.integer, src->value.logical);

  return result;
}


/* Convert integer to logical.  */

gfc_expr *
gfc_int2log (gfc_expr *src, int kind)
{
  gfc_expr *result;

  result = gfc_constant_result (BT_LOGICAL, kind, &src->where);
  result->value.logical = (mpz_cmp_si (src->value.integer, 0) != 0);

  return result;
}


/* Convert Hollerith to integer. The constant will be padded or truncated.  */

gfc_expr *
gfc_hollerith2int (gfc_expr * src, int kind)
{
  gfc_expr *result;
  int len;

  len = src->value.character.length;

  result = gfc_get_expr ();
  result->expr_type = EXPR_CONSTANT;
  result->ts.type = BT_INTEGER;
  result->ts.kind = kind;
  result->where = src->where;
  result->from_H = 1;

  if (len > kind)
    {
      gfc_warning ("The Hollerith constant at %L is too long to convert to %s",
		&src->where, gfc_typename(&result->ts));
    }
  result->value.character.string = gfc_getmem (kind + 1);
  memcpy (result->value.character.string, src->value.character.string,
	MIN (kind, len));

  if (len < kind)
    memset (&result->value.character.string[len], ' ', kind - len);

  result->value.character.string[kind] = '\0'; /* For debugger  */
  result->value.character.length = kind;

  return result;
}


/* Convert Hollerith to real. The constant will be padded or truncated.  */

gfc_expr *
gfc_hollerith2real (gfc_expr * src, int kind)
{
  gfc_expr *result;
  int len;

  len = src->value.character.length;

  result = gfc_get_expr ();
  result->expr_type = EXPR_CONSTANT;
  result->ts.type = BT_REAL;
  result->ts.kind = kind;
  result->where = src->where;
  result->from_H = 1;

  if (len > kind)
    {
      gfc_warning ("The Hollerith constant at %L is too long to convert to %s",
		&src->where, gfc_typename(&result->ts));
    }
  result->value.character.string = gfc_getmem (kind + 1);
  memcpy (result->value.character.string, src->value.character.string,
	MIN (kind, len));

  if (len < kind)
    memset (&result->value.character.string[len], ' ', kind - len);

  result->value.character.string[kind] = '\0'; /* For debugger.  */
  result->value.character.length = kind;

  return result;
}


/* Convert Hollerith to complex. The constant will be padded or truncated.  */

gfc_expr *
gfc_hollerith2complex (gfc_expr * src, int kind)
{
  gfc_expr *result;
  int len;

  len = src->value.character.length;

  result = gfc_get_expr ();
  result->expr_type = EXPR_CONSTANT;
  result->ts.type = BT_COMPLEX;
  result->ts.kind = kind;
  result->where = src->where;
  result->from_H = 1;

  kind = kind * 2;

  if (len > kind)
    {
      gfc_warning ("The Hollerith constant at %L is too long to convert to %s",
		&src->where, gfc_typename(&result->ts));
    }
  result->value.character.string = gfc_getmem (kind + 1);
  memcpy (result->value.character.string, src->value.character.string,
	MIN (kind, len));

  if (len < kind)
    memset (&result->value.character.string[len], ' ', kind - len);

  result->value.character.string[kind] = '\0'; /* For debugger  */
  result->value.character.length = kind;

  return result;
}


/* Convert Hollerith to character. */

gfc_expr *
gfc_hollerith2character (gfc_expr * src, int kind)
{
  gfc_expr *result;

  result = gfc_copy_expr (src);
  result->ts.type = BT_CHARACTER;
  result->ts.kind = kind;
  result->from_H = 1;

  return result;
}


/* Convert Hollerith to logical. The constant will be padded or truncated.  */

gfc_expr *
gfc_hollerith2logical (gfc_expr * src, int kind)
{
  gfc_expr *result;
  int len;

  len = src->value.character.length;

  result = gfc_get_expr ();
  result->expr_type = EXPR_CONSTANT;
  result->ts.type = BT_LOGICAL;
  result->ts.kind = kind;
  result->where = src->where;
  result->from_H = 1;

  if (len > kind)
    {
      gfc_warning ("The Hollerith constant at %L is too long to convert to %s",
		&src->where, gfc_typename(&result->ts));
    }
  result->value.character.string = gfc_getmem (kind + 1);
  memcpy (result->value.character.string, src->value.character.string,
	MIN (kind, len));

  if (len < kind)
    memset (&result->value.character.string[len], ' ', kind - len);

  result->value.character.string[kind] = '\0'; /* For debugger  */
  result->value.character.length = kind;

  return result;
}


/* Returns an initializer whose value is one higher than the value of the
   LAST_INITIALIZER argument.  If the argument is NULL, the
   initializers value will be set to zero.  The initializer's kind
   will be set to gfc_c_int_kind.

   If -fshort-enums is given, the appropriate kind will be selected
   later after all enumerators have been parsed.  A warning is issued
   here if an initializer exceeds gfc_c_int_kind.  */

gfc_expr *
gfc_enum_initializer (gfc_expr * last_initializer, locus where)
{
  gfc_expr *result;

  result = gfc_get_expr ();
  result->expr_type = EXPR_CONSTANT;
  result->ts.type = BT_INTEGER;
  result->ts.kind = gfc_c_int_kind;
  result->where = where;

  mpz_init (result->value.integer);

  if (last_initializer != NULL)
    {
      mpz_add_ui (result->value.integer, last_initializer->value.integer, 1);
      result->where = last_initializer->where;

      if (gfc_check_integer_range (result->value.integer,
             gfc_c_int_kind) != ARITH_OK)
        {
          gfc_error ("Enumerator exceeds the C integer type at %C");
          return NULL;
        }
    }
  else
    {
      /* Control comes here, if it's the very first enumerator and no
         initializer has been given.  It will be initialized to zero.  */
      mpz_set_si (result->value.integer, 0);
    }

  return result;
}