3.5.7 Floating Point Types
1
{floating point type}
For floating point types, the error bound is specified
as a relative precision by giving the required minimum number of significant
decimal digits.
Syntax
2
floating_point_definition ::=
digits static_expression [
real_range_specification]
3
real_range_specification ::=
range static_simple_expression ..
static_simple_expression
Name Resolution Rules
4
{requested decimal
precision (of a floating point type)} The
requested decimal precision, which is the minimum number of significant
decimal digits required for the floating point type, is specified by
the value of the
expression given after the
reserved word
digits.
{expected
type (requested decimal precision) [partial]} This
expression is expected to be of any integer
type.
5
{expected type (real_range_specification
bounds) [partial]} Each
simple_expression
of a
real_range_specification is expected
to be of any real type[; the types need not be the same].
Legality Rules
6
{Max_Base_Digits}
The requested decimal precision shall be specified
by a static
expression whose value is positive
and no greater than System.Max_Base_Digits. Each
simple_expression
of a
real_range_specification shall also be
static.
{Max_Digits} If
the
real_range_specification is omitted, the
requested decimal precision shall be no greater than System.Max_Digits.
6.a
Reason: We have added Max_Base_Digits
to package System. It corresponds to the requested decimal precision
of root_real. System.Max_Digits corresponds to the maximum value
for Digits that may be specified in the absence of a real_range_specification,
for upward compatibility. These might not be the same if root_real
has a base range that does not include ± 10.0**(4*Max_Base_Digits).
7
A floating_point_definition
is illegal if the implementation does not support a floating point type
that satisfies the requested decimal precision and range.
7.a
Implementation defined: What combinations
of requested decimal precision and range are supported for floating point
types.
Static Semantics
8
The set of values for a floating point type is the
(infinite) set of rational numbers.
{machine
numbers (of a floating point type)} The
machine numbers of a floating point type are the values of the
type that can be represented exactly in every unconstrained variable
of the type.
{base range (of a floating
point type) [partial]} The base range
(see
3.5) of a floating point type is symmetric
around zero, except that it can include some extra negative values in
some implementations.
8.a
Implementation Note: For example, if
a 2's complement representation is used for the mantissa rather than
a sign-mantissa or 1's complement representation, then there is usually
one extra negative machine number.
8.b
To be honest: If the Signed_Zeros attribute
is True, then minus zero could in a sense be considered a value of the
type. However, for most purposes, minus zero behaves the same as plus
zero.
9
{base decimal precision
(of a floating point type)} The
base
decimal precision of a floating point type is the number of decimal
digits of precision representable in objects of the type.
{safe
range (of a floating point type)} The
safe range of a floating point type is that part of its base range
for which the accuracy corresponding to the base decimal precision is
preserved by all predefined operations.
9.a
Implementation Note: In most cases, the
safe range and base range are the same. However, for some hardware, values
near the boundaries of the base range might result in excessive inaccuracies
or spurious overflows when used with certain predefined operations. For
such hardware, the safe range would omit such values.
10
{base decimal precision
(of a floating point type) [partial]} A
floating_point_definition defines a floating
point type whose base decimal precision is no less than the requested
decimal precision.
{safe range (of a
floating point type) [partial]} {base
range (of a floating point type) [partial]} If
a
real_range_specification is given, the safe
range of the floating point type (and hence, also its base range) includes
at least the values of the simple expressions given in the
real_range_specification.
If a
real_range_specification is not given,
the safe (and base) range of the type includes at least the values of
the range –10.0**(4*D) .. +10.0**(4*D) where D is the requested
decimal precision. [The safe range might include other values as well.
The attributes Safe_First and Safe_Last give the actual bounds of the
safe range.]
11
A
floating_point_definition
also defines a first subtype of the type.
{constrained
(subtype)} {unconstrained
(subtype)} If a
real_range_specification
is given, then the subtype is constrained to a range whose bounds are
given by a conversion of the values of the
simple_expressions
of the
real_range_specification to the type
being defined. Otherwise, the subtype is unconstrained.
11.a.1/1
To be honest: The
conversion mentioned above is not an implicit subtype conversion
(which is something that happens at overload resolution, see 4.6),
although it happens implicitly. Therefore, the freezing rules are not
invoked on the type (which is important so that representation items
can be given for the type). {subtype conversion (bounds of a floating
point type) [partial]}
12
{Float}
There is a predefined, unconstrained, floating point
subtype named Float[, declared in the visible part of package Standard].
Dynamic Semantics
13
{elaboration (floating_point_definition)
[partial]} [The elaboration of a
floating_point_definition
creates the floating point type and its first subtype.]
Implementation Requirements
14
{Float}
In an implementation that supports floating point
types with 6 or more digits of precision, the requested decimal precision
for Float shall be at least 6.
15
{Long_Float}
If Long_Float is predefined for an implementation,
then its requested decimal precision shall be at least 11.
Implementation Permissions
16
{Short_Float}
{Long_Float}
An implementation is allowed to provide additional
predefined floating point types[, declared in the visible part of Standard],
whose (unconstrained) first subtypes have names of the form Short_Float,
Long_Float, Short_Short_Float, Long_Long_Float, etc. Different predefined
floating point types are allowed to have the same base decimal precision.
However, the precision of Float should be no greater than that of Long_Float.
Similarly, the precision of Short_Float (if provided) should be no greater
than Float. Corresponding recommendations apply to any other predefined
floating point types. There need not be a named floating point type corresponding
to each distinct base decimal precision supported by an implementation.
16.a
Implementation defined: The predefined
floating point types declared in Standard.
Implementation Advice
17
{Long_Float}
An implementation should support Long_Float in addition
to Float if the target machine supports 11 or more digits of precision.
No other named floating point subtypes are recommended for package Standard.
Instead, appropriate named floating point subtypes should be provided
in the library package Interfaces (see
B.2).
17.a.1/2
Implementation Advice:
Long_Float should be declared in Standard
if the target supports 11 or more digits of precision. No other named
float subtypes should be declared in Standard.
17.a
Implementation Note: To promote portability,
implementations should explicitly declare the floating point (sub)types
Float and Long_Float in Standard, and leave other predefined float types
anonymous. For implementations that already support Short_Float, etc.,
upward compatibility argues for keeping such declarations in Standard
during the transition period, but perhaps generating a warning on use.
A separate package Interfaces in the predefined environment is available
for pre-declaring types such as Float_32, IEEE_Float_64, etc. See
B.2.
18
35 If a floating point subtype is unconstrained,
then assignments to variables of the subtype involve only Overflow_Checks,
never Range_Checks.
Examples
19
Examples of floating
point types and subtypes:
20
type Coefficient is digits 10 range -1.0 .. 1.0;
21
type Real is digits 8;
type Mass is digits 7 range 0.0 .. 1.0E35;
22
subtype Probability is Real range 0.0 .. 1.0; -- a subtype with a smaller range
Inconsistencies With Ada 83
22.a
{
inconsistencies with Ada 83}
No
Range_Checks, only Overflow_Checks, are performed on variables (or parameters)
of an unconstrained floating point subtype. This is upward compatible
for programs that do not raise Constraint_Error. For those that do raise
Constraint_Error, it is possible that the exception will be raised at
a later point, or not at all, if extended range floating point registers
are used to hold the value of the variable (or parameter).
22.b
Reason: This change was felt to be justified
by the possibility of improved performance on machines with extended-range
floating point registers. An implementation need not take advantage of
this relaxation in the range checking; it can hide completely the use
of extended range registers if desired, presumably at some run-time expense.
Wording Changes from Ada 83
22.c
The syntax rules for floating_point_constraint
and floating_accuracy_definition are removed.
The syntax rules for floating_point_definition
and real_range_specification are new.
22.d
A syntax rule for
digits_constraint
is given in
3.5.9, “
Fixed
Point Types”. In
J.3 we indicate
that a
digits_constraint may be applied to
a floating point
subtype_mark as well (to
be compatible with Ada 83's
floating_point_constraint).
22.e
Discussion of model numbers is postponed to
3.5.8 and
G.2.
The concept of safe numbers has been replaced by the concept of the safe
range of values. The bounds of the safe range are given by T'Safe_First
.. T'Safe_Last, rather than -T'Safe_Large .. T'Safe_Large, since on some
machines the safe range is not perfectly symmetric. The concept of machine
numbers is new, and is relevant to the definition of Succ and Pred for
floating point numbers.
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