numeric.c   [plain text]


/*    numeric.c
 *
 *    Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999,
 *    2000, 2001, 2002, 2003, by Larry Wall and others
 *
 *    You may distribute under the terms of either the GNU General Public
 *    License or the Artistic License, as specified in the README file.
 *
 */

/*
 * "That only makes eleven (plus one mislaid) and not fourteen, unless
 * wizards count differently to other people."
 */

/*
=head1 Numeric functions
*/

#include "EXTERN.h"
#define PERL_IN_NUMERIC_C
#include "perl.h"

U32
Perl_cast_ulong(pTHX_ NV f)
{
  if (f < 0.0)
    return f < I32_MIN ? (U32) I32_MIN : (U32)(I32) f;
  if (f < U32_MAX_P1) {
#if CASTFLAGS & 2
    if (f < U32_MAX_P1_HALF)
      return (U32) f;
    f -= U32_MAX_P1_HALF;
    return ((U32) f) | (1 + U32_MAX >> 1);
#else
    return (U32) f;
#endif
  }
  return f > 0 ? U32_MAX : 0 /* NaN */;
}

I32
Perl_cast_i32(pTHX_ NV f)
{
  if (f < I32_MAX_P1)
    return f < I32_MIN ? I32_MIN : (I32) f;
  if (f < U32_MAX_P1) {
#if CASTFLAGS & 2
    if (f < U32_MAX_P1_HALF)
      return (I32)(U32) f;
    f -= U32_MAX_P1_HALF;
    return (I32)(((U32) f) | (1 + U32_MAX >> 1));
#else
    return (I32)(U32) f;
#endif
  }
  return f > 0 ? (I32)U32_MAX : 0 /* NaN */;
}

IV
Perl_cast_iv(pTHX_ NV f)
{
  if (f < IV_MAX_P1)
    return f < IV_MIN ? IV_MIN : (IV) f;
  if (f < UV_MAX_P1) {
#if CASTFLAGS & 2
    /* For future flexibility allowing for sizeof(UV) >= sizeof(IV)  */
    if (f < UV_MAX_P1_HALF)
      return (IV)(UV) f;
    f -= UV_MAX_P1_HALF;
    return (IV)(((UV) f) | (1 + UV_MAX >> 1));
#else
    return (IV)(UV) f;
#endif
  }
  return f > 0 ? (IV)UV_MAX : 0 /* NaN */;
}

UV
Perl_cast_uv(pTHX_ NV f)
{
  if (f < 0.0)
    return f < IV_MIN ? (UV) IV_MIN : (UV)(IV) f;
  if (f < UV_MAX_P1) {
#if CASTFLAGS & 2
    if (f < UV_MAX_P1_HALF)
      return (UV) f;
    f -= UV_MAX_P1_HALF;
    return ((UV) f) | (1 + UV_MAX >> 1);
#else
    return (UV) f;
#endif
  }
  return f > 0 ? UV_MAX : 0 /* NaN */;
}

#if defined(HUGE_VAL) || (defined(USE_LONG_DOUBLE) && defined(HUGE_VALL))
/*
 * This hack is to force load of "huge" support from libm.a
 * So it is in perl for (say) POSIX to use.
 * Needed for SunOS with Sun's 'acc' for example.
 */
NV
Perl_huge(void)
{
#   if defined(USE_LONG_DOUBLE) && defined(HUGE_VALL)
    return HUGE_VALL;
#   endif
    return HUGE_VAL;
}
#endif

/*
=for apidoc grok_bin

converts a string representing a binary number to numeric form.

On entry I<start> and I<*len> give the string to scan, I<*flags> gives
conversion flags, and I<result> should be NULL or a pointer to an NV.
The scan stops at the end of the string, or the first invalid character.
On return I<*len> is set to the length scanned string, and I<*flags> gives
output flags.

If the value is <= UV_MAX it is returned as a UV, the output flags are clear,
and nothing is written to I<*result>. If the value is > UV_MAX C<grok_bin>
returns UV_MAX, sets C<PERL_SCAN_GREATER_THAN_UV_MAX> in the output flags,
and writes the value to I<*result> (or the value is discarded if I<result>
is NULL).

The hex number may optionally be prefixed with "0b" or "b" unless
C<PERL_SCAN_DISALLOW_PREFIX> is set in I<*flags> on entry. If
C<PERL_SCAN_ALLOW_UNDERSCORES> is set in I<*flags> then the binary
number may use '_' characters to separate digits.

=cut
 */

UV
Perl_grok_bin(pTHX_ char *start, STRLEN *len_p, I32 *flags, NV *result) {
    const char *s = start;
    STRLEN len = *len_p;
    UV value = 0;
    NV value_nv = 0;

    const UV max_div_2 = UV_MAX / 2;
    bool allow_underscores = *flags & PERL_SCAN_ALLOW_UNDERSCORES;
    bool overflowed = FALSE;

    if (!(*flags & PERL_SCAN_DISALLOW_PREFIX)) {
        /* strip off leading b or 0b.
           for compatibility silently suffer "b" and "0b" as valid binary
           numbers. */
        if (len >= 1) {
            if (s[0] == 'b') {
                s++;
                len--;
            }
            else if (len >= 2 && s[0] == '0' && s[1] == 'b') {
                s+=2;
                len-=2;
            }
        }
    }

    for (; len-- && *s; s++) {
        char bit = *s;
        if (bit == '0' || bit == '1') {
            /* Write it in this wonky order with a goto to attempt to get the
               compiler to make the common case integer-only loop pretty tight.
               With gcc seems to be much straighter code than old scan_bin.  */
          redo:
            if (!overflowed) {
                if (value <= max_div_2) {
                    value = (value << 1) | (bit - '0');
                    continue;
                }
                /* Bah. We're just overflowed.  */
                if (ckWARN_d(WARN_OVERFLOW))
                    Perl_warner(aTHX_ packWARN(WARN_OVERFLOW),
                                "Integer overflow in binary number");
                overflowed = TRUE;
                value_nv = (NV) value;
            }
            value_nv *= 2.0;
	    /* If an NV has not enough bits in its mantissa to
	     * represent a UV this summing of small low-order numbers
	     * is a waste of time (because the NV cannot preserve
	     * the low-order bits anyway): we could just remember when
	     * did we overflow and in the end just multiply value_nv by the
	     * right amount. */
            value_nv += (NV)(bit - '0');
            continue;
        }
        if (bit == '_' && len && allow_underscores && (bit = s[1])
            && (bit == '0' || bit == '1'))
	    {
		--len;
		++s;
                goto redo;
	    }
        if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT) && ckWARN(WARN_DIGIT))
            Perl_warner(aTHX_ packWARN(WARN_DIGIT),
                        "Illegal binary digit '%c' ignored", *s);
        break;
    }
    
    if (   ( overflowed && value_nv > 4294967295.0)
#if UVSIZE > 4
	|| (!overflowed && value > 0xffffffff  )
#endif
	) {
	if (ckWARN(WARN_PORTABLE))
	    Perl_warner(aTHX_ packWARN(WARN_PORTABLE),
			"Binary number > 0b11111111111111111111111111111111 non-portable");
    }
    *len_p = s - start;
    if (!overflowed) {
        *flags = 0;
        return value;
    }
    *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
    if (result)
        *result = value_nv;
    return UV_MAX;
}

/*
=for apidoc grok_hex

converts a string representing a hex number to numeric form.

On entry I<start> and I<*len> give the string to scan, I<*flags> gives
conversion flags, and I<result> should be NULL or a pointer to an NV.
The scan stops at the end of the string, or the first non-hex-digit character.
On return I<*len> is set to the length scanned string, and I<*flags> gives
output flags.

If the value is <= UV_MAX it is returned as a UV, the output flags are clear,
and nothing is written to I<*result>. If the value is > UV_MAX C<grok_hex>
returns UV_MAX, sets C<PERL_SCAN_GREATER_THAN_UV_MAX> in the output flags,
and writes the value to I<*result> (or the value is discarded if I<result>
is NULL).

The hex number may optionally be prefixed with "0x" or "x" unless
C<PERL_SCAN_DISALLOW_PREFIX> is set in I<*flags> on entry. If
C<PERL_SCAN_ALLOW_UNDERSCORES> is set in I<*flags> then the hex
number may use '_' characters to separate digits.

=cut
 */

UV
Perl_grok_hex(pTHX_ char *start, STRLEN *len_p, I32 *flags, NV *result) {
    const char *s = start;
    STRLEN len = *len_p;
    UV value = 0;
    NV value_nv = 0;

    const UV max_div_16 = UV_MAX / 16;
    bool allow_underscores = *flags & PERL_SCAN_ALLOW_UNDERSCORES;
    bool overflowed = FALSE;
    const char *hexdigit;

    if (!(*flags & PERL_SCAN_DISALLOW_PREFIX)) {
        /* strip off leading x or 0x.
           for compatibility silently suffer "x" and "0x" as valid hex numbers.
        */
        if (len >= 1) {
            if (s[0] == 'x') {
                s++;
                len--;
            }
            else if (len >= 2 && s[0] == '0' && s[1] == 'x') {
                s+=2;
                len-=2;
            }
        }
    }

    for (; len-- && *s; s++) {
	hexdigit = strchr((char *) PL_hexdigit, *s);
        if (hexdigit) {
            /* Write it in this wonky order with a goto to attempt to get the
               compiler to make the common case integer-only loop pretty tight.
               With gcc seems to be much straighter code than old scan_hex.  */
          redo:
            if (!overflowed) {
                if (value <= max_div_16) {
                    value = (value << 4) | ((hexdigit - PL_hexdigit) & 15);
                    continue;
                }
                /* Bah. We're just overflowed.  */
                if (ckWARN_d(WARN_OVERFLOW))
                    Perl_warner(aTHX_ packWARN(WARN_OVERFLOW),
                                "Integer overflow in hexadecimal number");
                overflowed = TRUE;
                value_nv = (NV) value;
            }
            value_nv *= 16.0;
	    /* If an NV has not enough bits in its mantissa to
	     * represent a UV this summing of small low-order numbers
	     * is a waste of time (because the NV cannot preserve
	     * the low-order bits anyway): we could just remember when
	     * did we overflow and in the end just multiply value_nv by the
	     * right amount of 16-tuples. */
            value_nv += (NV)((hexdigit - PL_hexdigit) & 15);
            continue;
        }
        if (*s == '_' && len && allow_underscores && s[1]
		&& (hexdigit = strchr((char *) PL_hexdigit, s[1])))
	    {
		--len;
		++s;
                goto redo;
	    }
        if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT) && ckWARN(WARN_DIGIT))
            Perl_warner(aTHX_ packWARN(WARN_DIGIT),
                        "Illegal hexadecimal digit '%c' ignored", *s);
        break;
    }
    
    if (   ( overflowed && value_nv > 4294967295.0)
#if UVSIZE > 4
	|| (!overflowed && value > 0xffffffff  )
#endif
	) {
	if (ckWARN(WARN_PORTABLE))
	    Perl_warner(aTHX_ packWARN(WARN_PORTABLE),
			"Hexadecimal number > 0xffffffff non-portable");
    }
    *len_p = s - start;
    if (!overflowed) {
        *flags = 0;
        return value;
    }
    *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
    if (result)
        *result = value_nv;
    return UV_MAX;
}

/*
=for apidoc grok_oct


=cut
 */

UV
Perl_grok_oct(pTHX_ char *start, STRLEN *len_p, I32 *flags, NV *result) {
    const char *s = start;
    STRLEN len = *len_p;
    UV value = 0;
    NV value_nv = 0;

    const UV max_div_8 = UV_MAX / 8;
    bool allow_underscores = *flags & PERL_SCAN_ALLOW_UNDERSCORES;
    bool overflowed = FALSE;

    for (; len-- && *s; s++) {
         /* gcc 2.95 optimiser not smart enough to figure that this subtraction
            out front allows slicker code.  */
        int digit = *s - '0';
        if (digit >= 0 && digit <= 7) {
            /* Write it in this wonky order with a goto to attempt to get the
               compiler to make the common case integer-only loop pretty tight.
            */
          redo:
            if (!overflowed) {
                if (value <= max_div_8) {
                    value = (value << 3) | digit;
                    continue;
                }
                /* Bah. We're just overflowed.  */
                if (ckWARN_d(WARN_OVERFLOW))
                    Perl_warner(aTHX_ packWARN(WARN_OVERFLOW),
                                "Integer overflow in octal number");
                overflowed = TRUE;
                value_nv = (NV) value;
            }
            value_nv *= 8.0;
	    /* If an NV has not enough bits in its mantissa to
	     * represent a UV this summing of small low-order numbers
	     * is a waste of time (because the NV cannot preserve
	     * the low-order bits anyway): we could just remember when
	     * did we overflow and in the end just multiply value_nv by the
	     * right amount of 8-tuples. */
            value_nv += (NV)digit;
            continue;
        }
        if (digit == ('_' - '0') && len && allow_underscores
            && (digit = s[1] - '0') && (digit >= 0 && digit <= 7))
	    {
		--len;
		++s;
                goto redo;
	    }
        /* Allow \octal to work the DWIM way (that is, stop scanning
         * as soon as non-octal characters are seen, complain only iff
         * someone seems to want to use the digits eight and nine). */
        if (digit == 8 || digit == 9) {
            if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT) && ckWARN(WARN_DIGIT))
                Perl_warner(aTHX_ packWARN(WARN_DIGIT),
                            "Illegal octal digit '%c' ignored", *s);
        }
        break;
    }
    
    if (   ( overflowed && value_nv > 4294967295.0)
#if UVSIZE > 4
	|| (!overflowed && value > 0xffffffff  )
#endif
	) {
	if (ckWARN(WARN_PORTABLE))
	    Perl_warner(aTHX_ packWARN(WARN_PORTABLE),
			"Octal number > 037777777777 non-portable");
    }
    *len_p = s - start;
    if (!overflowed) {
        *flags = 0;
        return value;
    }
    *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
    if (result)
        *result = value_nv;
    return UV_MAX;
}

/*
=for apidoc scan_bin

For backwards compatibility. Use C<grok_bin> instead.

=for apidoc scan_hex

For backwards compatibility. Use C<grok_hex> instead.

=for apidoc scan_oct

For backwards compatibility. Use C<grok_oct> instead.

=cut
 */

NV
Perl_scan_bin(pTHX_ char *start, STRLEN len, STRLEN *retlen)
{
    NV rnv;
    I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
    UV ruv = grok_bin (start, &len, &flags, &rnv);

    *retlen = len;
    return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
}

NV
Perl_scan_oct(pTHX_ char *start, STRLEN len, STRLEN *retlen)
{
    NV rnv;
    I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
    UV ruv = grok_oct (start, &len, &flags, &rnv);

    *retlen = len;
    return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
}

NV
Perl_scan_hex(pTHX_ char *start, STRLEN len, STRLEN *retlen)
{
    NV rnv;
    I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
    UV ruv = grok_hex (start, &len, &flags, &rnv);

    *retlen = len;
    return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
}

/*
=for apidoc grok_numeric_radix

Scan and skip for a numeric decimal separator (radix).

=cut
 */
bool
Perl_grok_numeric_radix(pTHX_ const char **sp, const char *send)
{
#ifdef USE_LOCALE_NUMERIC
    if (PL_numeric_radix_sv && IN_LOCALE) { 
        STRLEN len;
        char* radix = SvPV(PL_numeric_radix_sv, len);
        if (*sp + len <= send && memEQ(*sp, radix, len)) {
            *sp += len;
            return TRUE; 
        }
    }
    /* always try "." if numeric radix didn't match because
     * we may have data from different locales mixed */
#endif
    if (*sp < send && **sp == '.') {
        ++*sp;
        return TRUE;
    }
    return FALSE;
}

/*
=for apidoc grok_number

Recognise (or not) a number.  The type of the number is returned
(0 if unrecognised), otherwise it is a bit-ORed combination of
IS_NUMBER_IN_UV, IS_NUMBER_GREATER_THAN_UV_MAX, IS_NUMBER_NOT_INT,
IS_NUMBER_NEG, IS_NUMBER_INFINITY, IS_NUMBER_NAN (defined in perl.h).

If the value of the number can fit an in UV, it is returned in the *valuep
IS_NUMBER_IN_UV will be set to indicate that *valuep is valid, IS_NUMBER_IN_UV
will never be set unless *valuep is valid, but *valuep may have been assigned
to during processing even though IS_NUMBER_IN_UV is not set on return.
If valuep is NULL, IS_NUMBER_IN_UV will be set for the same cases as when
valuep is non-NULL, but no actual assignment (or SEGV) will occur.

IS_NUMBER_NOT_INT will be set with IS_NUMBER_IN_UV if trailing decimals were
seen (in which case *valuep gives the true value truncated to an integer), and
IS_NUMBER_NEG if the number is negative (in which case *valuep holds the
absolute value).  IS_NUMBER_IN_UV is not set if e notation was used or the
number is larger than a UV.

=cut
 */
int
Perl_grok_number(pTHX_ const char *pv, STRLEN len, UV *valuep)
{
  const char *s = pv;
  const char *send = pv + len;
  const UV max_div_10 = UV_MAX / 10;
  const char max_mod_10 = UV_MAX % 10;
  int numtype = 0;
  int sawinf = 0;
  int sawnan = 0;

  while (s < send && isSPACE(*s))
    s++;
  if (s == send) {
    return 0;
  } else if (*s == '-') {
    s++;
    numtype = IS_NUMBER_NEG;
  }
  else if (*s == '+')
  s++;

  if (s == send)
    return 0;

  /* next must be digit or the radix separator or beginning of infinity */
  if (isDIGIT(*s)) {
    /* UVs are at least 32 bits, so the first 9 decimal digits cannot
       overflow.  */
    UV value = *s - '0';
    /* This construction seems to be more optimiser friendly.
       (without it gcc does the isDIGIT test and the *s - '0' separately)
       With it gcc on arm is managing 6 instructions (6 cycles) per digit.
       In theory the optimiser could deduce how far to unroll the loop
       before checking for overflow.  */
    if (++s < send) {
      int digit = *s - '0';
      if (digit >= 0 && digit <= 9) {
        value = value * 10 + digit;
        if (++s < send) {
          digit = *s - '0';
          if (digit >= 0 && digit <= 9) {
            value = value * 10 + digit;
            if (++s < send) {
              digit = *s - '0';
              if (digit >= 0 && digit <= 9) {
                value = value * 10 + digit;
		if (++s < send) {
                  digit = *s - '0';
                  if (digit >= 0 && digit <= 9) {
                    value = value * 10 + digit;
                    if (++s < send) {
                      digit = *s - '0';
                      if (digit >= 0 && digit <= 9) {
                        value = value * 10 + digit;
                        if (++s < send) {
                          digit = *s - '0';
                          if (digit >= 0 && digit <= 9) {
                            value = value * 10 + digit;
                            if (++s < send) {
                              digit = *s - '0';
                              if (digit >= 0 && digit <= 9) {
                                value = value * 10 + digit;
                                if (++s < send) {
                                  digit = *s - '0';
                                  if (digit >= 0 && digit <= 9) {
                                    value = value * 10 + digit;
                                    if (++s < send) {
                                      /* Now got 9 digits, so need to check
                                         each time for overflow.  */
                                      digit = *s - '0';
                                      while (digit >= 0 && digit <= 9
                                             && (value < max_div_10
                                                 || (value == max_div_10
                                                     && digit <= max_mod_10))) {
                                        value = value * 10 + digit;
                                        if (++s < send)
                                          digit = *s - '0';
                                        else
                                          break;
                                      }
                                      if (digit >= 0 && digit <= 9
                                          && (s < send)) {
                                        /* value overflowed.
                                           skip the remaining digits, don't
                                           worry about setting *valuep.  */
                                        do {
                                          s++;
                                        } while (s < send && isDIGIT(*s));
                                        numtype |=
                                          IS_NUMBER_GREATER_THAN_UV_MAX;
                                        goto skip_value;
                                      }
                                    }
                                  }
				}
                              }
                            }
                          }
                        }
                      }
                    }
                  }
                }
              }
            }
          }
	}
      }
    }
    numtype |= IS_NUMBER_IN_UV;
    if (valuep)
      *valuep = value;

  skip_value:
    if (GROK_NUMERIC_RADIX(&s, send)) {
      numtype |= IS_NUMBER_NOT_INT;
      while (s < send && isDIGIT(*s))  /* optional digits after the radix */
        s++;
    }
  }
  else if (GROK_NUMERIC_RADIX(&s, send)) {
    numtype |= IS_NUMBER_NOT_INT | IS_NUMBER_IN_UV; /* valuep assigned below */
    /* no digits before the radix means we need digits after it */
    if (s < send && isDIGIT(*s)) {
      do {
        s++;
      } while (s < send && isDIGIT(*s));
      if (valuep) {
        /* integer approximation is valid - it's 0.  */
        *valuep = 0;
      }
    }
    else
      return 0;
  } else if (*s == 'I' || *s == 'i') {
    s++; if (s == send || (*s != 'N' && *s != 'n')) return 0;
    s++; if (s == send || (*s != 'F' && *s != 'f')) return 0;
    s++; if (s < send && (*s == 'I' || *s == 'i')) {
      s++; if (s == send || (*s != 'N' && *s != 'n')) return 0;
      s++; if (s == send || (*s != 'I' && *s != 'i')) return 0;
      s++; if (s == send || (*s != 'T' && *s != 't')) return 0;
      s++; if (s == send || (*s != 'Y' && *s != 'y')) return 0;
      s++;
    }
    sawinf = 1;
  } else if (*s == 'N' || *s == 'n') {
    /* XXX TODO: There are signaling NaNs and quiet NaNs. */
    s++; if (s == send || (*s != 'A' && *s != 'a')) return 0;
    s++; if (s == send || (*s != 'N' && *s != 'n')) return 0;
    s++;
    sawnan = 1;
  } else
    return 0;

  if (sawinf) {
    numtype &= IS_NUMBER_NEG; /* Keep track of sign  */
    numtype |= IS_NUMBER_INFINITY | IS_NUMBER_NOT_INT;
  } else if (sawnan) {
    numtype &= IS_NUMBER_NEG; /* Keep track of sign  */
    numtype |= IS_NUMBER_NAN | IS_NUMBER_NOT_INT;
  } else if (s < send) {
    /* we can have an optional exponent part */
    if (*s == 'e' || *s == 'E') {
      /* The only flag we keep is sign.  Blow away any "it's UV"  */
      numtype &= IS_NUMBER_NEG;
      numtype |= IS_NUMBER_NOT_INT;
      s++;
      if (s < send && (*s == '-' || *s == '+'))
        s++;
      if (s < send && isDIGIT(*s)) {
        do {
          s++;
        } while (s < send && isDIGIT(*s));
      }
      else
      return 0;
    }
  }
  while (s < send && isSPACE(*s))
    s++;
  if (s >= send)
    return numtype;
  if (len == 10 && memEQ(pv, "0 but true", 10)) {
    if (valuep)
      *valuep = 0;
    return IS_NUMBER_IN_UV;
  }
  return 0;
}

STATIC NV
S_mulexp10(NV value, I32 exponent)
{
    NV result = 1.0;
    NV power = 10.0;
    bool negative = 0;
    I32 bit;

    if (exponent == 0)
	return value;
    if (value == 0)
	return 0;

    /* On OpenVMS VAX we by default use the D_FLOAT double format,
     * and that format does not have *easy* capabilities [1] for
     * overflowing doubles 'silently' as IEEE fp does.  We also need 
     * to support G_FLOAT on both VAX and Alpha, and though the exponent 
     * range is much larger than D_FLOAT it still doesn't do silent 
     * overflow.  Therefore we need to detect early whether we would 
     * overflow (this is the behaviour of the native string-to-float 
     * conversion routines, and therefore of native applications, too).
     *
     * [1] Trying to establish a condition handler to trap floating point
     *     exceptions is not a good idea. */

    /* In UNICOS and in certain Cray models (such as T90) there is no
     * IEEE fp, and no way at all from C to catch fp overflows gracefully.
     * There is something you can do if you are willing to use some
     * inline assembler: the instruction is called DFI-- but that will
     * disable *all* floating point interrupts, a little bit too large
     * a hammer.  Therefore we need to catch potential overflows before
     * it's too late. */

#if ((defined(VMS) && !defined(__IEEE_FP)) || defined(_UNICOS)) && defined(NV_MAX_10_EXP)
    STMT_START {
	NV exp_v = log10(value);
	if (exponent >= NV_MAX_10_EXP || exponent + exp_v >= NV_MAX_10_EXP)
	    return NV_MAX;
	if (exponent < 0) {
	    if (-(exponent + exp_v) >= NV_MAX_10_EXP)
		return 0.0;
	    while (-exponent >= NV_MAX_10_EXP) {
		/* combination does not overflow, but 10^(-exponent) does */
		value /= 10;
		++exponent;
	    }
	}
    } STMT_END;
#endif

    if (exponent < 0) {
	negative = 1;
	exponent = -exponent;
    }
    for (bit = 1; exponent; bit <<= 1) {
	if (exponent & bit) {
	    exponent ^= bit;
	    result *= power;
	    /* Floating point exceptions are supposed to be turned off,
	     *  but if we're obviously done, don't risk another iteration.  
	     */
	     if (exponent == 0) break;
	}
	power *= power;
    }
    return negative ? value / result : value * result;
}

NV
Perl_my_atof(pTHX_ const char* s)
{
    NV x = 0.0;
#ifdef USE_LOCALE_NUMERIC
    if (PL_numeric_local && IN_LOCALE) {
	NV y;

	/* Scan the number twice; once using locale and once without;
	 * choose the larger result (in absolute value). */
	Perl_atof2(s, x);
	SET_NUMERIC_STANDARD();
	Perl_atof2(s, y);
	SET_NUMERIC_LOCAL();
	if ((y < 0.0 && y < x) || (y > 0.0 && y > x))
	    return y;
    }
    else
	Perl_atof2(s, x);
#else
    Perl_atof2(s, x);
#endif
    return x;
}

char*
Perl_my_atof2(pTHX_ const char* orig, NV* value)
{
    NV result[3] = {0.0, 0.0, 0.0};
    char* s = (char*)orig;
#ifdef USE_PERL_ATOF
    UV accumulator[2] = {0,0};	/* before/after dp */
    bool negative = 0;
    char* send = s + strlen(orig) - 1;
    bool seen_digit = 0;
    I32 exp_adjust[2] = {0,0};
    I32 exp_acc[2] = {-1, -1};
    /* the current exponent adjust for the accumulators */
    I32 exponent = 0;
    I32	seen_dp  = 0;
    I32 digit = 0;
    I32 old_digit = 0;
    I32 sig_digits = 0; /* noof significant digits seen so far */

/* There is no point in processing more significant digits
 * than the NV can hold. Note that NV_DIG is a lower-bound value,
 * while we need an upper-bound value. We add 2 to account for this;
 * since it will have been conservative on both the first and last digit.
 * For example a 32-bit mantissa with an exponent of 4 would have
 * exact values in the set
 *               4
 *               8
 *              ..
 *     17179869172
 *     17179869176
 *     17179869180
 *
 * where for the purposes of calculating NV_DIG we would have to discount
 * both the first and last digit, since neither can hold all values from
 * 0..9; but for calculating the value we must examine those two digits.
 */
#define MAX_SIG_DIGITS (NV_DIG+2)

/* the max number we can accumulate in a UV, and still safely do 10*N+9 */
#define MAX_ACCUMULATE ( (UV) ((UV_MAX - 9)/10))

    /* leading whitespace */
    while (isSPACE(*s))
	++s;

    /* sign */
    switch (*s) {
	case '-':
	    negative = 1;
	    /* fall through */
	case '+':
	    ++s;
    }

    /* we accumulate digits into an integer; when this becomes too
     * large, we add the total to NV and start again */

    while (1) {
	if (isDIGIT(*s)) {
	    seen_digit = 1;
	    old_digit = digit;
	    digit = *s++ - '0';
	    if (seen_dp)
		exp_adjust[1]++;

	    /* don't start counting until we see the first significant
	     * digit, eg the 5 in 0.00005... */
	    if (!sig_digits && digit == 0)
		continue;

	    if (++sig_digits > MAX_SIG_DIGITS) {
		/* limits of precision reached */
	        if (digit > 5) {
		    ++accumulator[seen_dp];
		} else if (digit == 5) {
		    if (old_digit % 2) { /* round to even - Allen */
			++accumulator[seen_dp];
		    }
		}
		if (seen_dp) {
		    exp_adjust[1]--;
		} else {
		    exp_adjust[0]++;
		}
		/* skip remaining digits */
		while (isDIGIT(*s)) {
		    ++s;
		    if (! seen_dp) {
			exp_adjust[0]++;
		    }
		}
		/* warn of loss of precision? */
	    }
	    else {
		if (accumulator[seen_dp] > MAX_ACCUMULATE) {
		    /* add accumulator to result and start again */
		    result[seen_dp] = S_mulexp10(result[seen_dp],
						 exp_acc[seen_dp])
			+ (NV)accumulator[seen_dp];
		    accumulator[seen_dp] = 0;
		    exp_acc[seen_dp] = 0;
		}
		accumulator[seen_dp] = accumulator[seen_dp] * 10 + digit;
		++exp_acc[seen_dp];
	    }
	}
	else if (!seen_dp && GROK_NUMERIC_RADIX((const char **)&s, send)) {
	    seen_dp = 1;
	    if (sig_digits > MAX_SIG_DIGITS) {
		++s;
		while (isDIGIT(*s)) {
		    ++s;
		}
		break;
	    }
	}
	else {
	    break;
	}
    }

    result[0] = S_mulexp10(result[0], exp_acc[0]) + (NV)accumulator[0];
    if (seen_dp) {
	result[1] = S_mulexp10(result[1], exp_acc[1]) + (NV)accumulator[1];
    }

    if (seen_digit && (*s == 'e' || *s == 'E')) {
	bool expnegative = 0;

	++s;
	switch (*s) {
	    case '-':
		expnegative = 1;
		/* fall through */
	    case '+':
		++s;
	}
	while (isDIGIT(*s))
	    exponent = exponent * 10 + (*s++ - '0');
	if (expnegative)
	    exponent = -exponent;
    }



    /* now apply the exponent */

    if (seen_dp) {
	result[2] = S_mulexp10(result[0],exponent+exp_adjust[0])
		+ S_mulexp10(result[1],exponent-exp_adjust[1]);
    } else {
	result[2] = S_mulexp10(result[0],exponent+exp_adjust[0]);
    }

    /* now apply the sign */
    if (negative)
	result[2] = -result[2];
#endif /* USE_PERL_ATOF */
    *value = result[2];
    return s;
}

#if ! defined(HAS_MODFL) && defined(HAS_AINTL) && defined(HAS_COPYSIGNL)
long double
Perl_my_modfl(long double x, long double *ip)
{
	*ip = aintl(x);
	return (x == *ip ? copysignl(0.0L, x) : x - *ip);
}
#endif

#if ! defined(HAS_FREXPL) && defined(HAS_ILOGBL) && defined(HAS_SCALBNL)
long double
Perl_my_frexpl(long double x, int *e) {
	*e = x == 0.0L ? 0 : ilogbl(x) + 1;
	return (scalbnl(x, -*e));
}
#endif