3.5.7 Floating Point Types
For floating point types, the
error bound is specified as a relative precision by giving the required
minimum number of significant decimal digits.
Name Resolution Rules
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
is expected to be of any integer type.
is illegal if the implementation does not support a floating point type
that satisfies the requested decimal precision and range.
The set of values for a floating point type is the
(infinite) set of rational numbers.
of a floating point type are the values of the type that
can be represented exactly in every unconstrained variable of the type.
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.
The base decimal precision
of a floating point type is the number of decimal digits of precision
representable in objects of the type.
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.
defines a floating point type whose base decimal precision is no less
than the requested decimal precision.
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.
There is a predefined, unconstrained,
floating point subtype named Float, declared in the visible part of package
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.
If Long_Float is predefined for
an implementation, then its requested decimal precision shall be at least
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.
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
35 If a floating point subtype is unconstrained,
then assignments to variables of the subtype involve only Overflow_Checks,
Examples of floating
point types and subtypes:
type Coefficient is digits 10 range -1.0 .. 1.0;
type Real is digits 8;
type Mass is digits 7 range 0.0 .. 1.0E35;
subtype Probability is Real range 0.0 .. 1.0; -- a subtype with a smaller range