The Standard ML Basis Library

The IEEEReal structure

Synopsis

signature IEEE_REAL
structure IEEEReal :> IEEE_REAL

The 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 [CITE] and the ANSI/IEEE standard 854-1987 [CITE] for additional information.

Interface

exception Unordered
datatype real_order = LESS | EQUAL | GREATER | UNORDERED
datatype float_class
  = NAN
  | 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 = {
                        class : float_class,
                        sign : bool,
                        digits : int list,
                        exp : int
                      }
val toString : decimal_approx -> string
val scan       : (char, 'a) StringCvt.reader
                   -> (decimal_approx, 'a) StringCvt.reader
val fromString : string -> decimal_approx option

Description

val setRoundingMode : rounding_mode -> unit
val getRoundingMode : unit -> rounding_mode
These set and get the rounding mode of the underlying hardware. The IEEE standard requires TO_NEAREST as the default rounding mode.

Implementation note:

Some platforms do not support all of the rounding modes. An SML implementation built on these platforms will necessarily be non-conforming with, presumably, setRoundingMode raising an exception for the unsupported modes.



type decimal_approx = {
                        class : float_class,
                        sign : bool,
                        digits : int list,
                        exp : int
                      }
This type provides a structured decimal representation of a real. The class 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 class is NORMAL or SUBNORMAL, a value 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 class is ZERO or INF, the value corresponds to zero or infinity, respectively, with its sign determined by sign. When class is NAN, the value corresponds to an unspecified NaN value.

toString d
returns a string representation of d. Assuming digits = [d(1), d(2), ..., d(n)] and ignoring the sign and exp fields, toString generates the following strings depending on the class field:
ZERO "0.0"
NORMAL "0.d(1)d(2)...d(n)"
SUBNORMAL "0.d(1)d(2)...d(n)"
INF "inf"
NAN "nan"
If the sign field is true, a #"~" is prepended. If the exp field is non-zero and the class is NORMAL or SUBNORMAL, the string "E"^(Integer.toString exp) is appended.

The composition toString o REAL.toDecimal is equivalent to REAL.fmt StringCvt.EXACT.

scan getc strm
fromString s
These functions scan a decimal approximation from a prefix of a character source. Initial whitespace is ignored. The first reads from the character stream src using the character input function getc. It returns SOME(d, rest) if the decimal approximation d can be parsed; rest is the remainder of the character stream. NONE is returned otherwise.

The second form uses the string s as input. It returns the decimal approximation on success and NONE otherwise. The fromString function is equivalent to StringCvt.scanString scan.

The functions accept real numbers with the following format:

[+~-]?([0-9]+.[0-9]+? | .[0-9]+)(e | E)[+~-]?[0-9]+?
The optional sign determines the value of the sign field, with a default of false. Initial zeros are stripped from the integer part and trailing zeros are stripped from the fractional part, yielding two lists il and fl, respectively, of digits. If il is non-empty, then class is set to NORMAL, digits is set to il@fl with any trailing zeros removed and exp is set to the length of il plus the value of the scanned exponent, if any. If il is empty and so is fl, then class is set to ZERO, digits = [] and exp = 0. Finally, if il is empty but fl is not, let m be the number of leading zeros in fl and let fl' be fl after the leading zeros are removed. Then, class is set to NORMAL, digits is set to fl' and exp is set to -m plus the value of the scanned exponent, if any.

They also accept the following string representations of non-finite values:

[+~-]?(inf | infinity | nan)
where the alphabetic characters are case-insensitive. The optional sign determines the value of the sign field, with a default of false. In the first and second cases, d will have class set to INF. In the third case, class is set to NAN. In all these cases, d will have digits = [] and exp = 0.

See Also

REAL, MATH

Discussion

Values of type decimal_approx are independent of any floating-point representation.

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Generated April 12, 2004
Last Modified January 28, 1997
Comments to John Reppy.

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