IEEEReal structureThe IEEEReal structure defines types associated with an IEEE implementation of floating-point numbers. In addition, it provides control for the floating-point hardware's rounding mode. Refer to the IEEE standard 754-1985 and the ANSI/IEEE standard 854-1987 for additional information.
signature IEEE_REAL
structure IEEEReal : IEEE_REAL
exception Unordered
datatype real_order = LESS | EQUAL | GREATER | UNORDERED
datatype nan_mode = QUIET | SIGNALLING
datatype float_class
= NAN of nan_mode
| INF
| ZERO
| NORMAL
| SUBNORMAL
datatype rounding_mode
= TO_NEAREST
| TO_NEGINF
| TO_POSINF
| TO_ZERO
val setRoundingMode : rounding_mode -> unit
val getRoundingMode : unit -> rounding_mode
type decimal_approx = { kind : float_class, sign : bool, digits : int list, exp : int }
val toString : decimal_approx -> string
val fromString : string -> decimal_approx option
exception Unordered
datatype real_order
datatype nan_mode
datatype float_class
datatype rounding_mode
setRoundingMode mode
getRoundingMode ()
type decimal_approx
kind field indicates the real class. If sign is true, the number is negative. The integers in the digits list must be digits, i.e., between 0 and 9.
When kind is NORMAL or SUBNORMAL, a value of of type decimal_approx with digits = [d(1), d(2), ..., d(n)] corresponds to the real number s * 0.d(1)d(2)...d(n) 10(exp), where s is -1 if sign is true and 1 otherwise. When kind is ZERO or INF, the value corresponds to zero or infinity, respectively, with its sign determined by sign. When kind is NAN _, the value corresponds to a NaN real value whose whose fraction bits are the binary equivalent of 0.d(1)d(2)...d(n) and whose sign bit is set if sign is true.
toString d
digits = [d(1), d(2), ..., d(n)] and ignoring the sign and exp fields, toString generates the following strings depending on the kind field:
| ZERO | 0.0 |
| NORMAL | 0.d(1)d(2)...d(n) |
| SUBNORMAL | 0.d(1)d(2)...d(n) |
| INF | inf |
| NAN _ | nan(d(1)d(2)...d(n)) |
sign field is true, a #"~" is prepended. If the exp field is non-zero and the kind is NORMAL or SUBNORMAL, the string "E"^(Integer.toString exp) is appended.
toString o REAL.toDecimal is equivalent to REAL.fmt IEEEReal.EXACT.
fromString s
SOME r if the decimal approximation r can be parsed from a prefix of string s, ignoring initial whitespace; NONE is returned if no such conversion is possible. fromString accepts any of the following regular expressions:
[+~-]?(INF|INFINITY)
[+~-]?(NAN|NAN\([0-9]+\))
[+~-]?(([0-9]+(\.[0-9]+)?)|(\.[0-9]+))([eE][+~-]?[0-9]+)?
where alphabetic characters are case-insensitive. The optional sign determines the value of the sign field, with a default of false. In the first case, kind is set to INF, digits = [] and exp = 0. In the second case, kind is set to NAN and exp = 0. If the optional digits are provided, they become the list of digits; otherwise, digits = []. In the last case, initial 0's are stripped from the integer part and trailing 0's are stripped from the fractional part, yielding two lists il and fl, respectively, of integers. If no digits are left, i.e., both lists are empty, kind is set to ZERO, digits = [] and exp = 0. Otherwise, kind is set to NORMAL, digits = il@fl, and exp is set to the length of il plus the value of the exponent, if it exists.
REAL, MATH
Last Modified January 28, 1997
Comments to John Reppy.
Copyright © 1997 Bell Labs, Lucent Technologies