3.3.2 Number Tokens

  • Article 
 INTEGER = integer-literal ["%" / "&" / "^"] 
 integer-literal = decimal-literal / octal-literal / hex-literal 
 decimal-literal = 1*decimal-digit 
 octal-literal = "&" [%x004F / %x006F] 1*octal-digit    ; & or &o or &O 
 hex-literal = "&" (%x0048 / %x0068) 1*hex-digit   ; &h or &H 
 octal-digit = "0" / "1" / "2" / "3" / "4" / "5" / "6" / "7" 
 decimal-digit = octal-digit / "8" / "9" 
 hex-digit = decimal-digit / %x0041-0046 / %x0061-0066 ;A-F / a-f

Static Semantics

  • The <decimal-digit>, <octal-digit>, and <hex-digit> sequences are interpreted as unsigned integer values represented respectively in decimal, octal, and hexadecimal notation.

  • Each <INTEGER> has an associated constant data value (section 2.1). The data value, value type (section 2.1) and declared type (section 2.2) of the constant is defined by the following table (if the Valid column shows No, this <INTEGER> is invalid):

    Radix

    Positive <INTEGER> value in the range

    Type Suffix

    Valid <INTEGER>?

    Declared Type

    Value Type

    Signed Data Value

    Decimal

    0 ≤ n ≤ 32767

    None

    Yes

    Integer

    Integer

    n

    Decimal

    0 ≤ n ≤ 32767

    "%"

    Yes

    Integer

    Integer

    n

    Decimal

    0 ≤ n ≤ 32767

    "&"

    Yes

    Long

    Integer

    n

    Decimal

    0 ≤ n ≤ 32767

    "^"

    Yes

    LongLong

    Integer

    n

    Octal

    0 ≤ n ≤ &o77777

    None

    Yes

    Integer

    Integer

    n

    Octal

    0 ≤ n ≤ &o77777

    "%"

    Yes

    Integer

    Integer

    n

    Octal

    0 ≤ n ≤ &o77777

    "&"

    Yes

    Long

    Integer

    n

    Octal

    0 ≤ n ≤ &o77777

    "^"

    Yes

    LongLong

    Integer

    n

    Octal

    &o100000 ≤ n ≤ &o177777

    None

    Yes

    Integer

    Integer

    n – 65,536

    Octal

    &o100000 ≤ n ≤ &o177777

    "%"

    Yes

    Integer

    Integer

    n – 65,536

    Octal

    &o100000 ≤ n ≤ &o177777

    "&"

    Yes

    Long

    Integer

    n

    Octal

    &o100000 ≤ n ≤ &o177777

    "^"

    Yes

    LongLong

    Integer

    n

    Hex

    0 ≤ n ≤ &H7FFF

    None

    Yes

    Integer

    Integer

    n

    Hex

    0 ≤ n ≤ &H7FFF

    "%"

    Yes

    Integer

    Integer

    n

    Hex

    0 ≤ n ≤ &H7FFF

    "&"

    Yes

    Long

    Integer

    n

    Hex

    0 ≤ n ≤ &H7FFF

    "^"

    Yes

    LongLong

    Integer

    n

    Hex

    &H8000 ≤ n ≤ &HFFFF

    None

    Yes

    Integer

    Integer

    n – 65,536

    Hex

    &H8000 ≤ n ≤ &HFFFF

    "%"

    Yes

    Integer

    Integer

    n – 65,536

    Hex

    &H8000 ≤ n ≤ &HFFFF

    "&"

    Yes

    Long

    Integer

    n

    Hex

    &H8000 ≤ n ≤ &HFFFF

    "^"

    Yes

    LongLong

    Integer

    n

    Decimal

    32768 ≤ n ≤ 2147483647

    None

    Yes

    Long

    Long

    n

    Decimal

    n ≥ 32768

    "%"

    No

    Decimal

    32768 ≤ n ≤ 2147483647

    "&"

    Yes

    Long

    Long

    n

    Decimal

    32768 ≤ n ≤ 2147483647

    "^"

    Yes

    LongLong

    Long

    n

    Decimal

    n ≥ 2147483647

    None

    (see note 1)

    Double

    Double

    n# (see note 1)

    Decimal

    n ≥ 2147483647

    "&"

    No

    Octal

    &o200000 ≤ n ≤ &o17777777777

    None

    Yes

    Long

    Long

    n

    Octal

    &o200000 ≤ n ≤ &o17777777777

    "%"

    No

    Octal

    &o200000 ≤ n ≤ &o17777777777

    "&"

    Yes

    Long

    Long

    n

    Octal

    &o200000 ≤ n ≤ &o17777777777

    "^"

    Yes

    LongLong

    Long

    n

    Octal

    &o20000000000 ≤ n ≤ &o37777777777

    None

    Yes

    Long

    Long

    n – 4,294,967,296

    Octal

    &o20000000000 ≤ n ≤ &o37777777777

    "%"

    No

    Octal

    &o20000000000 ≤ n ≤ &o37777777777

    "&"

    Yes

    Long

    Long

    n – 4,294,967,296

    Octal

    &o20000000000 ≤ n ≤ &o37777777777

    "^"

    Yes

    LongLong

    Long

    n

    Octal

    n ≥ &o40000000000

    None

    No

    Octal

    n ≥ &o40000000000

    "%"

    No

    Octal

    n ≥ &o40000000000

    "&"

    No

    Hex

    &H8000 ≤ n ≤ &H7FFFFFFF

    None

    Yes

    Long

    Long

    n

    Hex

    &H8000 ≤ n ≤ &H7FFFFFFF

    "%"

    No

    Hex

    &H8000 ≤ n ≤ &H7FFFFFFF

    "&"

    Yes

    Long

    Long

    n

    Hex

    &H8000 ≤ n ≤ &H7FFFFFFF

    "^"

    Yes

    LongLong

    Long

    n

    Hex

    &H80000000 ≤ n ≤ &H7FFFFFFFF

    None

    Yes

    Long

    Long

    n – 4,294,967,296

    Hex

    &H80000000 ≤ n ≤ &H7FFFFFFFF

    "%"

    No

    Hex

    &H80000000 ≤ n ≤ &H7FFFFFFFF

    "&"

    Yes

    Long

    Long

    n – 4,294,967,296

    Hex

    &H80000000 ≤ n ≤ &H7FFFFFFFF

    "^"

    Yes

    LongLong

    Long

    n

    Hex

    n ≥ &H100000000

    None

    No

    Hex

    n ≥ &H100000000

    "%"

    No

    Hex

    n ≥ &H100000000

    "&"

    No

    Decimal

    2147483648 ≤ n ≤ 9223372036854775807

    "^"

    Yes

    LongLong

    LongLong

    n

    Decimal

    n ≥ 9223372036854775808

    "^"

    Octal

    &o40000000000 ≤ n ≤ &o1777777777777777777777

    "^"

    Yes

    LongLong

    LongLong

    n - 232

    Octal

    n ≥ &o2000000000000000000000

    Any

    No

    Hex

    &H100000000 ≤ n ≤ &HFFFFFFFFFFFFFFFF

    "^"

    Yes

    LongLong

    LongLong

    n - 232

    Hex

    n ≥ &H10000000000000000

    Any

    No

  • It is statically invalid for a literal to have the declared type LongLong in an implementation that does not support 64-bit arithmetic. 

    FLOAT = (floating-point-literal [floating-point-type-suffix] ) / (decimal-literal floating-point-type-suffix) 
 floating-point-literal = (integer-digits exponent) / (integer-digits "." [fractional-digits] [exponent]) / ( "." fractional-digits [exponent])  
  
 integer-digits = decimal-literal 
 fractional-digits = decimal-literal 
 exponent = exponent-letter  [sign] decimal-literal 
 exponent-letter = %x0044 / %x0045 / %x0064 / %x0065   ; D / E / d / e  
 sign = "+" / "-"
 floating-point-type-suffix = "!" / "#" / "@"

Static Semantics

  • <FLOAT> tokens represent either binary floating point or currency data values. The <floatingpoint-type-suffix> designates the declared type and value type of the data value associated with the token according to the following table:

    <floating-point-type-suffix>

    Declared Type and Value Type

    Not present

    Double

    !

    Single

    #

    Double

    @

    Currency

    • Let i equal the integer value of <integer-digits>, f be the integer value of <fractional-digits>, d be the number of digits in <fractional-digits>, and x be the signed integer value of <exponent>. A <floating-point-literal> then represents a mathematical real number, r, according to this formula:

      Formula for the mathematical real number, r. R = open parentheses i + f times 10 to the minus d power closed parentheses 10 to the X power 

    • A <floating-point-literal> is invalid if its mathematical value is greater than the greatest mathematical value that can be represented using its declared type.

  • If the declared type of <floating-point-literal> is Currency, the fractional part of r is rounded using Banker’s rounding (section 5.5.1.2.1.1) to 4 significant digits.