Daily bump.

[official-gcc.git] / libcpp / expr.c

/* Parse C expressions for cpplib.
   Copyright (C) 1987, 1992, 1994, 1995, 1997, 1998, 1999, 2000, 2001,
   2002, 2004 Free Software Foundation.
   Contributed by Per Bothner, 1994.

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 program; if not, write to the Free Software
Foundation, 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.  */

#include "config.h"
#include "system.h"
#include "cpplib.h"
#include "internal.h"

#define PART_PRECISION (sizeof (cpp_num_part) * CHAR_BIT)
#define HALF_MASK (~(cpp_num_part) 0 >> (PART_PRECISION / 2))
#define LOW_PART(num_part) (num_part & HALF_MASK)
#define HIGH_PART(num_part) (num_part >> (PART_PRECISION / 2))

struct op
{
  const cpp_token *token;       /* The token forming op (for diagnostics).  */
  cpp_num value;                /* The value logically "right" of op.  */
  enum cpp_ttype op;
};

/* Some simple utility routines on double integers.  */
#define num_zerop(num) ((num.low | num.high) == 0)
#define num_eq(num1, num2) (num1.low == num2.low && num1.high == num2.high)
static bool num_positive (cpp_num, size_t);
static bool num_greater_eq (cpp_num, cpp_num, size_t);
static cpp_num num_trim (cpp_num, size_t);
static cpp_num num_part_mul (cpp_num_part, cpp_num_part);

static cpp_num num_unary_op (cpp_reader *, cpp_num, enum cpp_ttype);
static cpp_num num_binary_op (cpp_reader *, cpp_num, cpp_num, enum cpp_ttype);
static cpp_num num_negate (cpp_num, size_t);
static cpp_num num_bitwise_op (cpp_reader *, cpp_num, cpp_num, enum cpp_ttype);
static cpp_num num_inequality_op (cpp_reader *, cpp_num, cpp_num,
                                  enum cpp_ttype);
static cpp_num num_equality_op (cpp_reader *, cpp_num, cpp_num,
                                enum cpp_ttype);
static cpp_num num_mul (cpp_reader *, cpp_num, cpp_num);
static cpp_num num_div_op (cpp_reader *, cpp_num, cpp_num, enum cpp_ttype);
static cpp_num num_lshift (cpp_num, size_t, size_t);
static cpp_num num_rshift (cpp_num, size_t, size_t);

static cpp_num append_digit (cpp_num, int, int, size_t);
static cpp_num parse_defined (cpp_reader *);
static cpp_num eval_token (cpp_reader *, const cpp_token *);
static struct op *reduce (cpp_reader *, struct op *, enum cpp_ttype);
static unsigned int interpret_float_suffix (const uchar *, size_t);
static unsigned int interpret_int_suffix (const uchar *, size_t);
static void check_promotion (cpp_reader *, const struct op *);

/* Token type abuse to create unary plus and minus operators.  */
#define CPP_UPLUS ((enum cpp_ttype) (CPP_LAST_CPP_OP + 1))
#define CPP_UMINUS ((enum cpp_ttype) (CPP_LAST_CPP_OP + 2))

/* With -O2, gcc appears to produce nice code, moving the error
   message load and subsequent jump completely out of the main path.  */
#define SYNTAX_ERROR(msgid) \
  do { cpp_error (pfile, CPP_DL_ERROR, msgid); goto syntax_error; } while(0)
#define SYNTAX_ERROR2(msgid, arg) \
  do { cpp_error (pfile, CPP_DL_ERROR, msgid, arg); goto syntax_error; } \
  while(0)

/* Subroutine of cpp_classify_number.  S points to a float suffix of
   length LEN, possibly zero.  Returns 0 for an invalid suffix, or a
   flag vector describing the suffix.  */
static unsigned int
interpret_float_suffix (const uchar *s, size_t len)
{
  size_t f, l, w, q, i, d;

  f = l = w = q = i = d = 0;

  while (len--)
    switch (s[len])
      {
      case 'f': case 'F':
        if (d > 0)
          return 0;
        f++;
        break;
      case 'l': case 'L':
        if (d > 0)
          return 0;
        l++;
        break;
      case 'w': case 'W':
        if (d > 0)
          return 0;
        w++;
        break;
      case 'q': case 'Q':
        if (d > 0)
          return 0;
        q++;
        break;
      case 'i': case 'I':
      case 'j': case 'J': i++; break;
      case 'd': case 'D': d++; break;
      default:
        return 0;
      }

  if (f + l + w + q > 1 || i > 1)
    return 0;

  /* Allow dd, df, dl suffixes for decimal float constants.  */
  if (d && ((d + f + l != 2) || i))
    return 0;

  return ((i ? CPP_N_IMAGINARY : 0)
          | (f ? CPP_N_SMALL :
             l ? CPP_N_LARGE :
             w ? CPP_N_MD_W :
             q ? CPP_N_MD_Q : CPP_N_MEDIUM)
          | (d ? CPP_N_DFLOAT : 0));
}

/* Subroutine of cpp_classify_number.  S points to an integer suffix
   of length LEN, possibly zero. Returns 0 for an invalid suffix, or a
   flag vector describing the suffix.  */
static unsigned int
interpret_int_suffix (const uchar *s, size_t len)
{
  size_t u, l, i;

  u = l = i = 0;

  while (len--)
    switch (s[len])
      {
      case 'u': case 'U':       u++; break;
      case 'i': case 'I':
      case 'j': case 'J':       i++; break;
      case 'l': case 'L':       l++;
        /* If there are two Ls, they must be adjacent and the same case.  */
        if (l == 2 && s[len] != s[len + 1])
          return 0;
        break;
      default:
        return 0;
      }

  if (l > 2 || u > 1 || i > 1)
    return 0;

  return ((i ? CPP_N_IMAGINARY : 0)
          | (u ? CPP_N_UNSIGNED : 0)
          | ((l == 0) ? CPP_N_SMALL
             : (l == 1) ? CPP_N_MEDIUM : CPP_N_LARGE));
}

/* Categorize numeric constants according to their field (integer,
   floating point, or invalid), radix (decimal, octal, hexadecimal),
   and type suffixes.  */
unsigned int
cpp_classify_number (cpp_reader *pfile, const cpp_token *token)
{
  const uchar *str = token->val.str.text;
  const uchar *limit;
  unsigned int max_digit, result, radix;
  enum {NOT_FLOAT = 0, AFTER_POINT, AFTER_EXPON} float_flag;

  /* If the lexer has done its job, length one can only be a single
     digit.  Fast-path this very common case.  */
  if (token->val.str.len == 1)
    return CPP_N_INTEGER | CPP_N_SMALL | CPP_N_DECIMAL;

  limit = str + token->val.str.len;
  float_flag = NOT_FLOAT;
  max_digit = 0;
  radix = 10;

  /* First, interpret the radix.  */
  if (*str == '0')
    {
      radix = 8;
      str++;

      /* Require at least one hex digit to classify it as hex.  */
      if ((*str == 'x' || *str == 'X')
          && (str[1] == '.' || ISXDIGIT (str[1])))
        {
          radix = 16;
          str++;
        }
      else if ((*str == 'b' || *str == 'B') && (str[1] == '0' || str[1] == '1'))
        {
          radix = 2;
          str++;
        }
    }

  /* Now scan for a well-formed integer or float.  */
  for (;;)
    {
      unsigned int c = *str++;

      if (ISDIGIT (c) || (ISXDIGIT (c) && radix == 16))
        {
          c = hex_value (c);
          if (c > max_digit)
            max_digit = c;
        }
      else if (c == '.')
        {
          if (float_flag == NOT_FLOAT)
            float_flag = AFTER_POINT;
          else
            SYNTAX_ERROR ("too many decimal points in number");
        }
      else if ((radix <= 10 && (c == 'e' || c == 'E'))
               || (radix == 16 && (c == 'p' || c == 'P')))
        {
          float_flag = AFTER_EXPON;
          break;
        }
      else
        {
          /* Start of suffix.  */
          str--;
          break;
        }
    }

  if (float_flag != NOT_FLOAT && radix == 8)
    radix = 10;

  if (max_digit >= radix)
    {
      if (radix == 2)
        SYNTAX_ERROR2 ("invalid digit \"%c\" in binary constant", '0' + max_digit);
      else
        SYNTAX_ERROR2 ("invalid digit \"%c\" in octal constant", '0' + max_digit);
    }

  if (float_flag != NOT_FLOAT)
    {
      if (radix == 2)
        {
          cpp_error (pfile, CPP_DL_ERROR,
                     "invalid prefix \"0b\" for floating constant");
          return CPP_N_INVALID;
        }

      if (radix == 16 && CPP_PEDANTIC (pfile) && !CPP_OPTION (pfile, c99))
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "use of C99 hexadecimal floating constant");

      if (float_flag == AFTER_EXPON)
        {
          if (*str == '+' || *str == '-')
            str++;

          /* Exponent is decimal, even if string is a hex float.  */
          if (!ISDIGIT (*str))
            SYNTAX_ERROR ("exponent has no digits");

          do
            str++;
          while (ISDIGIT (*str));
        }
      else if (radix == 16)
        SYNTAX_ERROR ("hexadecimal floating constants require an exponent");

      result = interpret_float_suffix (str, limit - str);
      if (result == 0)
        {
          cpp_error (pfile, CPP_DL_ERROR,
                     "invalid suffix \"%.*s\" on floating constant",
                     (int) (limit - str), str);
          return CPP_N_INVALID;
        }

      /* Traditional C didn't accept any floating suffixes.  */
      if (limit != str
          && CPP_WTRADITIONAL (pfile)
          && ! cpp_sys_macro_p (pfile))
        cpp_error (pfile, CPP_DL_WARNING,
                   "traditional C rejects the \"%.*s\" suffix",
                   (int) (limit - str), str);

      /* Radix must be 10 for decimal floats.  */
      if ((result & CPP_N_DFLOAT) && radix != 10)
        {
          cpp_error (pfile, CPP_DL_ERROR,
                     "invalid suffix \"%.*s\" with hexadecimal floating constant",
                     (int) (limit - str), str);
          return CPP_N_INVALID;
        }

      if ((result & CPP_N_DFLOAT) && CPP_PEDANTIC (pfile))
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "decimal float constants are a GCC extension");

      result |= CPP_N_FLOATING;
    }
  else
    {
      result = interpret_int_suffix (str, limit - str);
      if (result == 0)
        {
          cpp_error (pfile, CPP_DL_ERROR,
                     "invalid suffix \"%.*s\" on integer constant",
                     (int) (limit - str), str);
          return CPP_N_INVALID;
        }

      /* Traditional C only accepted the 'L' suffix.
         Suppress warning about 'LL' with -Wno-long-long.  */
      if (CPP_WTRADITIONAL (pfile) && ! cpp_sys_macro_p (pfile))
        {
          int u_or_i = (result & (CPP_N_UNSIGNED|CPP_N_IMAGINARY));
          int large = (result & CPP_N_WIDTH) == CPP_N_LARGE;

          if (u_or_i || (large && CPP_OPTION (pfile, warn_long_long)))
            cpp_error (pfile, CPP_DL_WARNING,
                       "traditional C rejects the \"%.*s\" suffix",
                       (int) (limit - str), str);
        }

      if ((result & CPP_N_WIDTH) == CPP_N_LARGE
          && ! CPP_OPTION (pfile, c99)
          && CPP_OPTION (pfile, warn_long_long))
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "use of C99 long long integer constant");

      result |= CPP_N_INTEGER;
    }

  if ((result & CPP_N_IMAGINARY) && CPP_PEDANTIC (pfile))
    cpp_error (pfile, CPP_DL_PEDWARN,
               "imaginary constants are a GCC extension");
  if (radix == 2 && CPP_PEDANTIC (pfile))
    cpp_error (pfile, CPP_DL_PEDWARN,
               "binary constants are a GCC extension");

  if (radix == 10)
    result |= CPP_N_DECIMAL;
  else if (radix == 16)
    result |= CPP_N_HEX;
  else if (radix == 2)
    result |= CPP_N_BINARY;
  else
    result |= CPP_N_OCTAL;

  return result;

 syntax_error:
  return CPP_N_INVALID;
}

/* cpp_interpret_integer converts an integer constant into a cpp_num,
   of precision options->precision.

   We do not provide any interface for decimal->float conversion,
   because the preprocessor doesn't need it and we don't want to
   drag in GCC's floating point emulator.  */
cpp_num
cpp_interpret_integer (cpp_reader *pfile, const cpp_token *token,
                       unsigned int type)
{
  const uchar *p, *end;
  cpp_num result;

  result.low = 0;
  result.high = 0;
  result.unsignedp = !!(type & CPP_N_UNSIGNED);
  result.overflow = false;

  p = token->val.str.text;
  end = p + token->val.str.len;

  /* Common case of a single digit.  */
  if (token->val.str.len == 1)
    result.low = p[0] - '0';
  else
    {
      cpp_num_part max;
      size_t precision = CPP_OPTION (pfile, precision);
      unsigned int base = 10, c = 0;
      bool overflow = false;

      if ((type & CPP_N_RADIX) == CPP_N_OCTAL)
        {
          base = 8;
          p++;
        }
      else if ((type & CPP_N_RADIX) == CPP_N_HEX)
        {
          base = 16;
          p += 2;
        }
      else if ((type & CPP_N_RADIX) == CPP_N_BINARY)
        {
          base = 2;
          p += 2;
        }

      /* We can add a digit to numbers strictly less than this without
         needing the precision and slowness of double integers.  */
      max = ~(cpp_num_part) 0;
      if (precision < PART_PRECISION)
        max >>= PART_PRECISION - precision;
      max = (max - base + 1) / base + 1;

      for (; p < end; p++)
        {
          c = *p;

          if (ISDIGIT (c) || (base == 16 && ISXDIGIT (c)))
            c = hex_value (c);
          else
            break;

          /* Strict inequality for when max is set to zero.  */
          if (result.low < max)
            result.low = result.low * base + c;
          else
            {
              result = append_digit (result, c, base, precision);
              overflow |= result.overflow;
              max = 0;
            }
        }

      if (overflow)
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "integer constant is too large for its type");
      /* If too big to be signed, consider it unsigned.  Only warn for
         decimal numbers.  Traditional numbers were always signed (but
         we still honor an explicit U suffix); but we only have
         traditional semantics in directives.  */
      else if (!result.unsignedp
               && !(CPP_OPTION (pfile, traditional)
                    && pfile->state.in_directive)
               && !num_positive (result, precision))
        {
          if (base == 10)
            cpp_error (pfile, CPP_DL_WARNING,
                       "integer constant is so large that it is unsigned");
          result.unsignedp = true;
        }
    }

  return result;
}

/* Append DIGIT to NUM, a number of PRECISION bits being read in base BASE.  */
static cpp_num
append_digit (cpp_num num, int digit, int base, size_t precision)
{
  cpp_num result;
  unsigned int shift;
  bool overflow;
  cpp_num_part add_high, add_low;

  /* Multiply by 2, 8 or 16.  Catching this overflow here means we don't
     need to worry about add_high overflowing.  */
  switch (base)
    {
    case 2:
      shift = 1;
      break;

    case 16:
      shift = 4;
      break;

    default:
      shift = 3;
    }
  overflow = !!(num.high >> (PART_PRECISION - shift));
  result.high = num.high << shift;
  result.low = num.low << shift;
  result.high |= num.low >> (PART_PRECISION - shift);
  result.unsignedp = num.unsignedp;

  if (base == 10)
    {
      add_low = num.low << 1;
      add_high = (num.high << 1) + (num.low >> (PART_PRECISION - 1));
    }
  else
    add_high = add_low = 0;

  if (add_low + digit < add_low)
    add_high++;
  add_low += digit;

  if (result.low + add_low < result.low)
    add_high++;
  if (result.high + add_high < result.high)
    overflow = true;

  result.low += add_low;
  result.high += add_high;
  result.overflow = overflow;

  /* The above code catches overflow of a cpp_num type.  This catches
     overflow of the (possibly shorter) target precision.  */
  num.low = result.low;
  num.high = result.high;
  result = num_trim (result, precision);
  if (!num_eq (result, num))
    result.overflow = true;

  return result;
}

/* Handle meeting "defined" in a preprocessor expression.  */
static cpp_num
parse_defined (cpp_reader *pfile)
{
  cpp_num result;
  int paren = 0;
  cpp_hashnode *node = 0;
  const cpp_token *token;
  cpp_context *initial_context = pfile->context;

  /* Don't expand macros.  */
  pfile->state.prevent_expansion++;

  token = cpp_get_token (pfile);
  if (token->type == CPP_OPEN_PAREN)
    {
      paren = 1;
      token = cpp_get_token (pfile);
    }

  if (token->type == CPP_NAME)
    {
      node = token->val.node;
      if (paren && cpp_get_token (pfile)->type != CPP_CLOSE_PAREN)
        {
          cpp_error (pfile, CPP_DL_ERROR, "missing ')' after \"defined\"");
          node = 0;
        }
    }
  else
    {
      cpp_error (pfile, CPP_DL_ERROR,
                 "operator \"defined\" requires an identifier");
      if (token->flags & NAMED_OP)
        {
          cpp_token op;

          op.flags = 0;
          op.type = token->type;
          cpp_error (pfile, CPP_DL_ERROR,
                     "(\"%s\" is an alternative token for \"%s\" in C++)",
                     cpp_token_as_text (pfile, token),
                     cpp_token_as_text (pfile, &op));
        }
    }

  if (node)
    {
      if (pfile->context != initial_context && CPP_PEDANTIC (pfile))
        cpp_error (pfile, CPP_DL_WARNING,
                   "this use of \"defined\" may not be portable");

      _cpp_mark_macro_used (node);

      /* A possible controlling macro of the form #if !defined ().
         _cpp_parse_expr checks there was no other junk on the line.  */
      pfile->mi_ind_cmacro = node;
    }

  pfile->state.prevent_expansion--;

  result.unsignedp = false;
  result.high = 0;
  result.overflow = false;
  result.low = node && node->type == NT_MACRO;
  return result;
}

/* Convert a token into a CPP_NUMBER (an interpreted preprocessing
   number or character constant, or the result of the "defined" or "#"
   operators).  */
static cpp_num
eval_token (cpp_reader *pfile, const cpp_token *token)
{
  cpp_num result;
  unsigned int temp;
  int unsignedp = 0;

  result.unsignedp = false;
  result.overflow = false;

  switch (token->type)
    {
    case CPP_NUMBER:
      temp = cpp_classify_number (pfile, token);
      switch (temp & CPP_N_CATEGORY)
        {
        case CPP_N_FLOATING:
          cpp_error (pfile, CPP_DL_ERROR,
                     "floating constant in preprocessor expression");
          break;
        case CPP_N_INTEGER:
          if (!(temp & CPP_N_IMAGINARY))
            return cpp_interpret_integer (pfile, token, temp);
          cpp_error (pfile, CPP_DL_ERROR,
                     "imaginary number in preprocessor expression");
          break;

        case CPP_N_INVALID:
          /* Error already issued.  */
          break;
        }
      result.high = result.low = 0;
      break;

    case CPP_WCHAR:
    case CPP_CHAR:
      {
        cppchar_t cc = cpp_interpret_charconst (pfile, token,
                                                &temp, &unsignedp);

        result.high = 0;
        result.low = cc;
        /* Sign-extend the result if necessary.  */
        if (!unsignedp && (cppchar_signed_t) cc < 0)
          {
            if (PART_PRECISION > BITS_PER_CPPCHAR_T)
              result.low |= ~(~(cpp_num_part) 0
                              >> (PART_PRECISION - BITS_PER_CPPCHAR_T));
            result.high = ~(cpp_num_part) 0;
            result = num_trim (result, CPP_OPTION (pfile, precision));
          }
      }
      break;

    case CPP_NAME:
      if (token->val.node == pfile->spec_nodes.n_defined)
        return parse_defined (pfile);
      else if (CPP_OPTION (pfile, cplusplus)
               && (token->val.node == pfile->spec_nodes.n_true
                   || token->val.node == pfile->spec_nodes.n_false))
        {
          result.high = 0;
          result.low = (token->val.node == pfile->spec_nodes.n_true);
        }
      else
        {
          result.high = 0;
          result.low = 0;
          if (CPP_OPTION (pfile, warn_undef) && !pfile->state.skip_eval)
            cpp_error (pfile, CPP_DL_WARNING, "\"%s\" is not defined",
                       NODE_NAME (token->val.node));
        }
      break;

    default: /* CPP_HASH */
      _cpp_test_assertion (pfile, &temp);
      result.high = 0;
      result.low = temp;
    }

  result.unsignedp = !!unsignedp;
  return result;
}
\f
/* Operator precedence and flags table.

After an operator is returned from the lexer, if it has priority less
than the operator on the top of the stack, we reduce the stack by one
operator and repeat the test.  Since equal priorities do not reduce,
this is naturally right-associative.

We handle left-associative operators by decrementing the priority of
just-lexed operators by one, but retaining the priority of operators
already on the stack.

The remaining cases are '(' and ')'.  We handle '(' by skipping the
reduction phase completely.  ')' is given lower priority than
everything else, including '(', effectively forcing a reduction of the
parenthesized expression.  If there is a matching '(', the routine
reduce() exits immediately.  If the normal exit route sees a ')', then
there cannot have been a matching '(' and an error message is output.

The parser assumes all shifted operators require a left operand unless
the flag NO_L_OPERAND is set.  These semantics are automatic; any
extra semantics need to be handled with operator-specific code.  */

/* Flags.  If CHECK_PROMOTION, we warn if the effective sign of an
   operand changes because of integer promotions.  */
#define NO_L_OPERAND    (1 << 0)
#define LEFT_ASSOC      (1 << 1)
#define CHECK_PROMOTION (1 << 2)

/* Operator to priority map.  Must be in the same order as the first
   N entries of enum cpp_ttype.  */
static const struct cpp_operator
{
  uchar prio;
  uchar flags;
} optab[] =
{
  /* EQ */              {0, 0}, /* Shouldn't happen.  */
  /* NOT */             {16, NO_L_OPERAND},
  /* GREATER */         {12, LEFT_ASSOC | CHECK_PROMOTION},
  /* LESS */            {12, LEFT_ASSOC | CHECK_PROMOTION},
  /* PLUS */            {14, LEFT_ASSOC | CHECK_PROMOTION},
  /* MINUS */           {14, LEFT_ASSOC | CHECK_PROMOTION},
  /* MULT */            {15, LEFT_ASSOC | CHECK_PROMOTION},
  /* DIV */             {15, LEFT_ASSOC | CHECK_PROMOTION},
  /* MOD */             {15, LEFT_ASSOC | CHECK_PROMOTION},
  /* AND */             {9, LEFT_ASSOC | CHECK_PROMOTION},
  /* OR */              {7, LEFT_ASSOC | CHECK_PROMOTION},
  /* XOR */             {8, LEFT_ASSOC | CHECK_PROMOTION},
  /* RSHIFT */          {13, LEFT_ASSOC},
  /* LSHIFT */          {13, LEFT_ASSOC},

  /* COMPL */           {16, NO_L_OPERAND},
  /* AND_AND */         {6, LEFT_ASSOC},
  /* OR_OR */           {5, LEFT_ASSOC},
  /* QUERY */           {3, 0},
  /* COLON */           {4, LEFT_ASSOC | CHECK_PROMOTION},
  /* COMMA */           {2, LEFT_ASSOC},
  /* OPEN_PAREN */      {1, NO_L_OPERAND},
  /* CLOSE_PAREN */     {0, 0},
  /* EOF */             {0, 0},
  /* EQ_EQ */           {11, LEFT_ASSOC},
  /* NOT_EQ */          {11, LEFT_ASSOC},
  /* GREATER_EQ */      {12, LEFT_ASSOC | CHECK_PROMOTION},
  /* LESS_EQ */         {12, LEFT_ASSOC | CHECK_PROMOTION},
  /* UPLUS */           {16, NO_L_OPERAND},
  /* UMINUS */          {16, NO_L_OPERAND}
};

/* Parse and evaluate a C expression, reading from PFILE.
   Returns the truth value of the expression.

   The implementation is an operator precedence parser, i.e. a
   bottom-up parser, using a stack for not-yet-reduced tokens.

   The stack base is op_stack, and the current stack pointer is 'top'.
   There is a stack element for each operator (only), and the most
   recently pushed operator is 'top->op'.  An operand (value) is
   stored in the 'value' field of the stack element of the operator
   that precedes it.  */
bool
_cpp_parse_expr (cpp_reader *pfile)
{
  struct op *top = pfile->op_stack;
  unsigned int lex_count;
  bool saw_leading_not, want_value = true;

  pfile->state.skip_eval = 0;

  /* Set up detection of #if ! defined().  */
  pfile->mi_ind_cmacro = 0;
  saw_leading_not = false;
  lex_count = 0;

  /* Lowest priority operator prevents further reductions.  */
  top->op = CPP_EOF;

  for (;;)
    {
      struct op op;

      lex_count++;
      op.token = cpp_get_token (pfile);
      op.op = op.token->type;

      switch (op.op)
        {
          /* These tokens convert into values.  */
        case CPP_NUMBER:
        case CPP_CHAR:
        case CPP_WCHAR:
        case CPP_NAME:
        case CPP_HASH:
          if (!want_value)
            SYNTAX_ERROR2 ("missing binary operator before token \"%s\"",
                           cpp_token_as_text (pfile, op.token));
          want_value = false;
          top->value = eval_token (pfile, op.token);
          continue;

        case CPP_NOT:
          saw_leading_not = lex_count == 1;
          break;
        case CPP_PLUS:
          if (want_value)
            op.op = CPP_UPLUS;
          break;
        case CPP_MINUS:
          if (want_value)
            op.op = CPP_UMINUS;
          break;

        default:
          if ((int) op.op <= (int) CPP_EQ || (int) op.op >= (int) CPP_PLUS_EQ)
            SYNTAX_ERROR2 ("token \"%s\" is not valid in preprocessor expressions",
                           cpp_token_as_text (pfile, op.token));
          break;
        }

      /* Check we have a value or operator as appropriate.  */
      if (optab[op.op].flags & NO_L_OPERAND)
        {
          if (!want_value)
            SYNTAX_ERROR2 ("missing binary operator before token \"%s\"",
                           cpp_token_as_text (pfile, op.token));
        }
      else if (want_value)
        {
          /* We want a number (or expression) and haven't got one.
             Try to emit a specific diagnostic.  */
          if (op.op == CPP_CLOSE_PAREN && top->op == CPP_OPEN_PAREN)
            SYNTAX_ERROR ("missing expression between '(' and ')'");

          if (op.op == CPP_EOF && top->op == CPP_EOF)
            SYNTAX_ERROR ("#if with no expression");

          if (top->op != CPP_EOF && top->op != CPP_OPEN_PAREN)
            SYNTAX_ERROR2 ("operator '%s' has no right operand",
                           cpp_token_as_text (pfile, top->token));
          else if (op.op == CPP_CLOSE_PAREN || op.op == CPP_EOF)
            /* Complain about missing paren during reduction.  */;
          else
            SYNTAX_ERROR2 ("operator '%s' has no left operand",
                           cpp_token_as_text (pfile, op.token));
        }

      top = reduce (pfile, top, op.op);
      if (!top)
        goto syntax_error;

      if (op.op == CPP_EOF)
        break;

      switch (op.op)
        {
        case CPP_CLOSE_PAREN:
          continue;
        case CPP_OR_OR:
          if (!num_zerop (top->value))
            pfile->state.skip_eval++;
          break;
        case CPP_AND_AND:
        case CPP_QUERY:
          if (num_zerop (top->value))
            pfile->state.skip_eval++;
          break;
        case CPP_COLON:
          if (top->op != CPP_QUERY)
            SYNTAX_ERROR (" ':' without preceding '?'");
          if (!num_zerop (top[-1].value)) /* Was '?' condition true?  */
            pfile->state.skip_eval++;
          else
            pfile->state.skip_eval--;
        default:
          break;
        }

      want_value = true;

      /* Check for and handle stack overflow.  */
      if (++top == pfile->op_limit)
        top = _cpp_expand_op_stack (pfile);

      top->op = op.op;
      top->token = op.token;
    }

  /* The controlling macro expression is only valid if we called lex 3
     times: <!> <defined expression> and <EOF>.  push_conditional ()
     checks that we are at top-of-file.  */
  if (pfile->mi_ind_cmacro && !(saw_leading_not && lex_count == 3))
    pfile->mi_ind_cmacro = 0;

  if (top != pfile->op_stack)
    {
      cpp_error (pfile, CPP_DL_ICE, "unbalanced stack in #if");
    syntax_error:
      return false;  /* Return false on syntax error.  */
    }

  return !num_zerop (top->value);
}

/* Reduce the operator / value stack if possible, in preparation for
   pushing operator OP.  Returns NULL on error, otherwise the top of
   the stack.  */
static struct op *
reduce (cpp_reader *pfile, struct op *top, enum cpp_ttype op)
{
  unsigned int prio;

  if (top->op <= CPP_EQ || top->op > CPP_LAST_CPP_OP + 2)
    {
    bad_op:
      cpp_error (pfile, CPP_DL_ICE, "impossible operator '%u'", top->op);
      return 0;
    }

  if (op == CPP_OPEN_PAREN)
    return top;

  /* Decrement the priority of left-associative operators to force a
     reduction with operators of otherwise equal priority.  */
  prio = optab[op].prio - ((optab[op].flags & LEFT_ASSOC) != 0);
  while (prio < optab[top->op].prio)
    {
      if (CPP_OPTION (pfile, warn_num_sign_change)
          && optab[top->op].flags & CHECK_PROMOTION)
        check_promotion (pfile, top);

      switch (top->op)
        {
        case CPP_UPLUS:
        case CPP_UMINUS:
        case CPP_NOT:
        case CPP_COMPL:
          top[-1].value = num_unary_op (pfile, top->value, top->op);
          break;

        case CPP_PLUS:
        case CPP_MINUS:
        case CPP_RSHIFT:
        case CPP_LSHIFT:
        case CPP_COMMA:
          top[-1].value = num_binary_op (pfile, top[-1].value,
                                         top->value, top->op);
          break;

        case CPP_GREATER:
        case CPP_LESS:
        case CPP_GREATER_EQ:
        case CPP_LESS_EQ:
          top[-1].value
            = num_inequality_op (pfile, top[-1].value, top->value, top->op);
          break;

        case CPP_EQ_EQ:
        case CPP_NOT_EQ:
          top[-1].value
            = num_equality_op (pfile, top[-1].value, top->value, top->op);
          break;

        case CPP_AND:
        case CPP_OR:
        case CPP_XOR:
          top[-1].value
            = num_bitwise_op (pfile, top[-1].value, top->value, top->op);
          break;

        case CPP_MULT:
          top[-1].value = num_mul (pfile, top[-1].value, top->value);
          break;

        case CPP_DIV:
        case CPP_MOD:
          top[-1].value = num_div_op (pfile, top[-1].value,
                                      top->value, top->op);
          break;

        case CPP_OR_OR:
          top--;
          if (!num_zerop (top->value))
            pfile->state.skip_eval--;
          top->value.low = (!num_zerop (top->value)
                            || !num_zerop (top[1].value));
          top->value.high = 0;
          top->value.unsignedp = false;
          top->value.overflow = false;
          continue;

        case CPP_AND_AND:
          top--;
          if (num_zerop (top->value))
            pfile->state.skip_eval--;
          top->value.low = (!num_zerop (top->value)
                            && !num_zerop (top[1].value));
          top->value.high = 0;
          top->value.unsignedp = false;
          top->value.overflow = false;
          continue;

        case CPP_OPEN_PAREN:
          if (op != CPP_CLOSE_PAREN)
            {
              cpp_error (pfile, CPP_DL_ERROR, "missing ')' in expression");
              return 0;
            }
          top--;
          top->value = top[1].value;
          return top;

        case CPP_COLON:
          top -= 2;
          if (!num_zerop (top->value))
            {
              pfile->state.skip_eval--;
              top->value = top[1].value;
            }
          else
            top->value = top[2].value;
          top->value.unsignedp = (top[1].value.unsignedp
                                  || top[2].value.unsignedp);
          continue;

        case CPP_QUERY:
          cpp_error (pfile, CPP_DL_ERROR, "'?' without following ':'");
          return 0;

        default:
          goto bad_op;
        }

      top--;
      if (top->value.overflow && !pfile->state.skip_eval)
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "integer overflow in preprocessor expression");
    }

  if (op == CPP_CLOSE_PAREN)
    {
      cpp_error (pfile, CPP_DL_ERROR, "missing '(' in expression");
      return 0;
    }

  return top;
}

/* Returns the position of the old top of stack after expansion.  */
struct op *
_cpp_expand_op_stack (cpp_reader *pfile)
{
  size_t old_size = (size_t) (pfile->op_limit - pfile->op_stack);
  size_t new_size = old_size * 2 + 20;

  pfile->op_stack = XRESIZEVEC (struct op, pfile->op_stack, new_size);
  pfile->op_limit = pfile->op_stack + new_size;

  return pfile->op_stack + old_size;
}

/* Emits a warning if the effective sign of either operand of OP
   changes because of integer promotions.  */
static void
check_promotion (cpp_reader *pfile, const struct op *op)
{
  if (op->value.unsignedp == op[-1].value.unsignedp)
    return;

  if (op->value.unsignedp)
    {
      if (!num_positive (op[-1].value, CPP_OPTION (pfile, precision)))
        cpp_error (pfile, CPP_DL_WARNING,
                   "the left operand of \"%s\" changes sign when promoted",
                   cpp_token_as_text (pfile, op->token));
    }
  else if (!num_positive (op->value, CPP_OPTION (pfile, precision)))
    cpp_error (pfile, CPP_DL_WARNING,
               "the right operand of \"%s\" changes sign when promoted",
               cpp_token_as_text (pfile, op->token));
}

/* Clears the unused high order bits of the number pointed to by PNUM.  */
static cpp_num
num_trim (cpp_num num, size_t precision)
{
  if (precision > PART_PRECISION)
    {
      precision -= PART_PRECISION;
      if (precision < PART_PRECISION)
        num.high &= ((cpp_num_part) 1 << precision) - 1;
    }
  else
    {
      if (precision < PART_PRECISION)
        num.low &= ((cpp_num_part) 1 << precision) - 1;
      num.high = 0;
    }

  return num;
}

/* True iff A (presumed signed) >= 0.  */
static bool
num_positive (cpp_num num, size_t precision)
{
  if (precision > PART_PRECISION)
    {
      precision -= PART_PRECISION;
      return (num.high & (cpp_num_part) 1 << (precision - 1)) == 0;
    }

  return (num.low & (cpp_num_part) 1 << (precision - 1)) == 0;
}

/* Sign extend a number, with PRECISION significant bits and all
   others assumed clear, to fill out a cpp_num structure.  */
cpp_num
cpp_num_sign_extend (cpp_num num, size_t precision)
{
  if (!num.unsignedp)
    {
      if (precision > PART_PRECISION)
        {
          precision -= PART_PRECISION;
          if (precision < PART_PRECISION
              && (num.high & (cpp_num_part) 1 << (precision - 1)))
            num.high |= ~(~(cpp_num_part) 0 >> (PART_PRECISION - precision));
        }
      else if (num.low & (cpp_num_part) 1 << (precision - 1))
        {
          if (precision < PART_PRECISION)
            num.low |= ~(~(cpp_num_part) 0 >> (PART_PRECISION - precision));
          num.high = ~(cpp_num_part) 0;
        }
    }

  return num;
}

/* Returns the negative of NUM.  */
static cpp_num
num_negate (cpp_num num, size_t precision)
{
  cpp_num copy;

  copy = num;
  num.high = ~num.high;
  num.low = ~num.low;
  if (++num.low == 0)
    num.high++;
  num = num_trim (num, precision);
  num.overflow = (!num.unsignedp && num_eq (num, copy) && !num_zerop (num));

  return num;
}

/* Returns true if A >= B.  */
static bool
num_greater_eq (cpp_num pa, cpp_num pb, size_t precision)
{
  bool unsignedp;

  unsignedp = pa.unsignedp || pb.unsignedp;

  if (!unsignedp)
    {
      /* Both numbers have signed type.  If they are of different
       sign, the answer is the sign of A.  */
      unsignedp = num_positive (pa, precision);

      if (unsignedp != num_positive (pb, precision))
        return unsignedp;

      /* Otherwise we can do an unsigned comparison.  */
    }

  return (pa.high > pb.high) || (pa.high == pb.high && pa.low >= pb.low);
}

/* Returns LHS OP RHS, where OP is a bit-wise operation.  */
static cpp_num
num_bitwise_op (cpp_reader *pfile ATTRIBUTE_UNUSED,
                cpp_num lhs, cpp_num rhs, enum cpp_ttype op)
{
  lhs.overflow = false;
  lhs.unsignedp = lhs.unsignedp || rhs.unsignedp;

  /* As excess precision is zeroed, there is no need to num_trim () as
     these operations cannot introduce a set bit there.  */
  if (op == CPP_AND)
    {
      lhs.low &= rhs.low;
      lhs.high &= rhs.high;
    }
  else if (op == CPP_OR)
    {
      lhs.low |= rhs.low;
      lhs.high |= rhs.high;
    }
  else
    {
      lhs.low ^= rhs.low;
      lhs.high ^= rhs.high;
    }

  return lhs;
}

/* Returns LHS OP RHS, where OP is an inequality.  */
static cpp_num
num_inequality_op (cpp_reader *pfile, cpp_num lhs, cpp_num rhs,
                   enum cpp_ttype op)
{
  bool gte = num_greater_eq (lhs, rhs, CPP_OPTION (pfile, precision));

  if (op == CPP_GREATER_EQ)
    lhs.low = gte;
  else if (op == CPP_LESS)
    lhs.low = !gte;
  else if (op == CPP_GREATER)
    lhs.low = gte && !num_eq (lhs, rhs);
  else /* CPP_LESS_EQ.  */
    lhs.low = !gte || num_eq (lhs, rhs);

  lhs.high = 0;
  lhs.overflow = false;
  lhs.unsignedp = false;
  return lhs;
}

/* Returns LHS OP RHS, where OP is == or !=.  */
static cpp_num
num_equality_op (cpp_reader *pfile ATTRIBUTE_UNUSED,
                 cpp_num lhs, cpp_num rhs, enum cpp_ttype op)
{
  /* Work around a 3.0.4 bug; see PR 6950.  */
  bool eq = num_eq (lhs, rhs);
  if (op == CPP_NOT_EQ)
    eq = !eq;
  lhs.low = eq;
  lhs.high = 0;
  lhs.overflow = false;
  lhs.unsignedp = false;
  return lhs;
}

/* Shift NUM, of width PRECISION, right by N bits.  */
static cpp_num
num_rshift (cpp_num num, size_t precision, size_t n)
{
  cpp_num_part sign_mask;
  bool x = num_positive (num, precision);

  if (num.unsignedp || x)
    sign_mask = 0;
  else
    sign_mask = ~(cpp_num_part) 0;

  if (n >= precision)
    num.high = num.low = sign_mask;
  else
    {
      /* Sign-extend.  */
      if (precision < PART_PRECISION)
        num.high = sign_mask, num.low |= sign_mask << precision;
      else if (precision < 2 * PART_PRECISION)
        num.high |= sign_mask << (precision - PART_PRECISION);

      if (n >= PART_PRECISION)
        {
          n -= PART_PRECISION;
          num.low = num.high;
          num.high = sign_mask;
        }

      if (n)
        {
          num.low = (num.low >> n) | (num.high << (PART_PRECISION - n));
          num.high = (num.high >> n) | (sign_mask << (PART_PRECISION - n));
        }
    }

  num = num_trim (num, precision);
  num.overflow = false;
  return num;
}

/* Shift NUM, of width PRECISION, left by N bits.  */
static cpp_num
num_lshift (cpp_num num, size_t precision, size_t n)
{
  if (n >= precision)
    {
      num.overflow = !num.unsignedp && !num_zerop (num);
      num.high = num.low = 0;
    }
  else
    {
      cpp_num orig, maybe_orig;
      size_t m = n;

      orig = num;
      if (m >= PART_PRECISION)
        {
          m -= PART_PRECISION;
          num.high = num.low;
          num.low = 0;
        }
      if (m)
        {
          num.high = (num.high << m) | (num.low >> (PART_PRECISION - m));
          num.low <<= m;
        }
      num = num_trim (num, precision);

      if (num.unsignedp)
        num.overflow = false;
      else
        {
          maybe_orig = num_rshift (num, precision, n);
          num.overflow = !num_eq (orig, maybe_orig);
        }
    }

  return num;
}

/* The four unary operators: +, -, ! and ~.  */
static cpp_num
num_unary_op (cpp_reader *pfile, cpp_num num, enum cpp_ttype op)
{
  switch (op)
    {
    case CPP_UPLUS:
      if (CPP_WTRADITIONAL (pfile) && !pfile->state.skip_eval)
        cpp_error (pfile, CPP_DL_WARNING,
                   "traditional C rejects the unary plus operator");
      num.overflow = false;
      break;

    case CPP_UMINUS:
      num = num_negate (num, CPP_OPTION (pfile, precision));
      break;

    case CPP_COMPL:
      num.high = ~num.high;
      num.low = ~num.low;
      num = num_trim (num, CPP_OPTION (pfile, precision));
      num.overflow = false;
      break;

    default: /* case CPP_NOT: */
      num.low = num_zerop (num);
      num.high = 0;
      num.overflow = false;
      num.unsignedp = false;
      break;
    }

  return num;
}

/* The various binary operators.  */
static cpp_num
num_binary_op (cpp_reader *pfile, cpp_num lhs, cpp_num rhs, enum cpp_ttype op)
{
  cpp_num result;
  size_t precision = CPP_OPTION (pfile, precision);
  size_t n;

  switch (op)
    {
      /* Shifts.  */
    case CPP_LSHIFT:
    case CPP_RSHIFT:
      if (!rhs.unsignedp && !num_positive (rhs, precision))
        {
          /* A negative shift is a positive shift the other way.  */
          if (op == CPP_LSHIFT)
            op = CPP_RSHIFT;
          else
            op = CPP_LSHIFT;
          rhs = num_negate (rhs, precision);
        }
      if (rhs.high)
        n = ~0;                 /* Maximal.  */
      else
        n = rhs.low;
      if (op == CPP_LSHIFT)
        lhs = num_lshift (lhs, precision, n);
      else
        lhs = num_rshift (lhs, precision, n);
      break;

      /* Arithmetic.  */
    case CPP_MINUS:
      rhs = num_negate (rhs, precision);
    case CPP_PLUS:
      result.low = lhs.low + rhs.low;
      result.high = lhs.high + rhs.high;
      if (result.low < lhs.low)
        result.high++;
      result.unsignedp = lhs.unsignedp || rhs.unsignedp;
      result.overflow = false;

      result = num_trim (result, precision);
      if (!result.unsignedp)
        {
          bool lhsp = num_positive (lhs, precision);
          result.overflow = (lhsp == num_positive (rhs, precision)
                             && lhsp != num_positive (result, precision));
        }
      return result;

      /* Comma.  */
    default: /* case CPP_COMMA: */
      if (CPP_PEDANTIC (pfile) && (!CPP_OPTION (pfile, c99)
                                   || !pfile->state.skip_eval))
        cpp_error (pfile, CPP_DL_PEDWARN,
                   "comma operator in operand of #if");
      lhs = rhs;
      break;
    }

  return lhs;
}

/* Multiplies two unsigned cpp_num_parts to give a cpp_num.  This
   cannot overflow.  */
static cpp_num
num_part_mul (cpp_num_part lhs, cpp_num_part rhs)
{
  cpp_num result;
  cpp_num_part middle[2], temp;

  result.low = LOW_PART (lhs) * LOW_PART (rhs);
  result.high = HIGH_PART (lhs) * HIGH_PART (rhs);

  middle[0] = LOW_PART (lhs) * HIGH_PART (rhs);
  middle[1] = HIGH_PART (lhs) * LOW_PART (rhs);

  temp = result.low;
  result.low += LOW_PART (middle[0]) << (PART_PRECISION / 2);
  if (result.low < temp)
    result.high++;

  temp = result.low;
  result.low += LOW_PART (middle[1]) << (PART_PRECISION / 2);
  if (result.low < temp)
    result.high++;

  result.high += HIGH_PART (middle[0]);
  result.high += HIGH_PART (middle[1]);
  result.unsignedp = true;
  result.overflow = false;

  return result;
}

/* Multiply two preprocessing numbers.  */
static cpp_num
num_mul (cpp_reader *pfile, cpp_num lhs, cpp_num rhs)
{
  cpp_num result, temp;
  bool unsignedp = lhs.unsignedp || rhs.unsignedp;
  bool overflow, negate = false;
  size_t precision = CPP_OPTION (pfile, precision);

  /* Prepare for unsigned multiplication.  */
  if (!unsignedp)
    {
      if (!num_positive (lhs, precision))
        negate = !negate, lhs = num_negate (lhs, precision);
      if (!num_positive (rhs, precision))
        negate = !negate, rhs = num_negate (rhs, precision);
    }

  overflow = lhs.high && rhs.high;
  result = num_part_mul (lhs.low, rhs.low);

  temp = num_part_mul (lhs.high, rhs.low);
  result.high += temp.low;
  if (temp.high)
    overflow = true;

  temp = num_part_mul (lhs.low, rhs.high);
  result.high += temp.low;
  if (temp.high)
    overflow = true;

  temp.low = result.low, temp.high = result.high;
  result = num_trim (result, precision);
  if (!num_eq (result, temp))
    overflow = true;

  if (negate)
    result = num_negate (result, precision);

  if (unsignedp)
    result.overflow = false;
  else
    result.overflow = overflow || (num_positive (result, precision) ^ !negate
                                   && !num_zerop (result));
  result.unsignedp = unsignedp;

  return result;
}

/* Divide two preprocessing numbers, returning the answer or the
   remainder depending upon OP.  */
static cpp_num
num_div_op (cpp_reader *pfile, cpp_num lhs, cpp_num rhs, enum cpp_ttype op)
{
  cpp_num result, sub;
  cpp_num_part mask;
  bool unsignedp = lhs.unsignedp || rhs.unsignedp;
  bool negate = false, lhs_neg = false;
  size_t i, precision = CPP_OPTION (pfile, precision);

  /* Prepare for unsigned division.  */
  if (!unsignedp)
    {
      if (!num_positive (lhs, precision))
        negate = !negate, lhs_neg = true, lhs = num_negate (lhs, precision);
      if (!num_positive (rhs, precision))
        negate = !negate, rhs = num_negate (rhs, precision);
    }

  /* Find the high bit.  */
  if (rhs.high)
    {
      i = precision - 1;
      mask = (cpp_num_part) 1 << (i - PART_PRECISION);
      for (; ; i--, mask >>= 1)
        if (rhs.high & mask)
          break;
    }
  else if (rhs.low)
    {
      if (precision > PART_PRECISION)
        i = precision - PART_PRECISION - 1;
      else
        i = precision - 1;
      mask = (cpp_num_part) 1 << i;
      for (; ; i--, mask >>= 1)
        if (rhs.low & mask)
          break;
    }
  else
    {
      if (!pfile->state.skip_eval)
        cpp_error (pfile, CPP_DL_ERROR, "division by zero in #if");
      return lhs;
    }

  /* First nonzero bit of RHS is bit I.  Do naive division by
     shifting the RHS fully left, and subtracting from LHS if LHS is
     at least as big, and then repeating but with one less shift.
     This is not very efficient, but is easy to understand.  */

  rhs.unsignedp = true;
  lhs.unsignedp = true;
  i = precision - i - 1;
  sub = num_lshift (rhs, precision, i);

  result.high = result.low = 0;
  for (;;)
    {
      if (num_greater_eq (lhs, sub, precision))
        {
          lhs = num_binary_op (pfile, lhs, sub, CPP_MINUS);
          if (i >= PART_PRECISION)
            result.high |= (cpp_num_part) 1 << (i - PART_PRECISION);
          else
            result.low |= (cpp_num_part) 1 << i;
        }
      if (i-- == 0)
        break;
      sub.low = (sub.low >> 1) | (sub.high << (PART_PRECISION - 1));
      sub.high >>= 1;
    }

  /* We divide so that the remainder has the sign of the LHS.  */
  if (op == CPP_DIV)
    {
      result.unsignedp = unsignedp;
      result.overflow = false;
      if (!unsignedp)
        {
          if (negate)
            result = num_negate (result, precision);
          result.overflow = (num_positive (result, precision) ^ !negate
                             && !num_zerop (result));
        }

      return result;
    }

  /* CPP_MOD.  */
  lhs.unsignedp = unsignedp;
  lhs.overflow = false;
  if (lhs_neg)
    lhs = num_negate (lhs, precision);

  return lhs;
}