IEEEReal
structure
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.
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
val setRoundingMode : rounding_mode -> unit
val getRoundingMode : unit -> rounding_mode
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
}
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
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" |
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
is equivalent to toString
o REAL.toDecimal
.
REAL.fmt
StringCvt.EXACT
scan getc strm
fromString s
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
.
REAL
,MATH
Values of type decimal_approx
are independent of any floating-point representation.
Generated April 12, 2004
Last Modified January 28, 1997
Comments to John Reppy.
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