Re: delta?

Re: delta?

[David C. Hoos, Sr.]

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yukchi wrote in message <7b9bl7$ki5$1@eng-ser1.erg.cuhk.edu.hk>...
>hihi
>what is the meaning of delta and digits in the following sentence?
>type Money is delta 0.01 digits 15;
>thanks in advance!
>

It's defined by the relevant section of the Ada Language Reference Manual,
excerpted here:

3.5.9 Fixed Point Types

1 A fixed point type is either an ordinary fixed point type, or a decimal
fixed point type. The error bound of a fixed point type is specified as an
absolute value, called the delta of the fixed point type.

Syntax

2 fixed_point_definition ::= ordinary_fixed_point_definition |
decimal_fixed_point_definition
3 ordinary_fixed_point_definition ::=
delta static_expression  real_range_specification
4 decimal_fixed_point_definition ::=
delta static_expression digits static_expression [real_range_specification]
5 digits_constraint ::=
digits static_expression [range_constraint]

Name Resolution Rules

6 For a type defined by a fixed_point_definition, the delta of the type is
specified by the value of the expression given after the reserved word
delta; this expression is expected to be of any real type. For a type
defined by a decimal_fixed_point_definition (a decimal fixed point type),
the number of significant decimal digits for its first subtype (the digits
of the first subtype) is specified by the expression given after the
reserved word digits; this expression is expected to be of any integer type.

Legality Rules

7 In a fixed_point_definition or digits_constraint, the expressions given
after the reserved words delta and digits shall be static; their values
shall be positive.
8 The set of values of a fixed point type comprise the integral multiples of
a number called the small of the type. For a type defined by an
ordinary_fixed_point_definition (an ordinary fixed point type), the small
may be specified by an attribute_definition_clause (see 13.3); if so
specified, it shall be no greater than the delta of the type. If not
specified, the small of an ordinary fixed point type is an
implementation-defined power of two less than or equal to the delta.

9 For a decimal fixed point type, the small equals the delta; the delta
shall be a power of 10. If a real_range_specification is given, both bounds
of the range shall be in the range �(10**digits�1)*delta ..
+(10**digits�1)*delta.
10 A fixed_point_definition is illegal if the implementation does not
support a fixed point type with the given small and specified range or
digits.

11 For a subtype_indication with a digits_constraint, the subtype_mark shall
denote a decimal fixed point subtype.

Static Semantics

12 The base range (see 3.5) of a fixed point type is symmetric around zero,
except possibly for an extra negative value in some implementations.
13 An ordinary_fixed_point_definition defines an ordinary fixed point type
whose base range includes at least all multiples of small that are between
the bounds specified in the real_range_specification. The base range of the
type does not necessarily include the specified bounds themselves. An
ordinary_fixed_point_definition also defines a constrained first subtype of
the type, with each bound of its range given by the closer to zero of:

14 � the value of the conversion to the fixed point type of the
corresponding expression of the real_range_specification;
15 � the corresponding bound of the base range.

16 A decimal_fixed_point_definition defines a decimal fixed point type whose
base range includes at least the range �(10**digits�1)*
delta .. +(10**digits�1)*delta. A decimal_fixed_point_definition also
defines a constrained first subtype of the type. If a
real_range_specification is given, the bounds of the first subtype are given
by a conversion of the values of the expressions of the
real_range_specification. Otherwise, the range of the first subtype
is �(10**digits�1)*delta .. +(10**digits�1)*delta.

Dynamic Semantics

17 The elaboration of a fixed_point_definition creates the fixed point type
and its first subtype.
18 For a digits_constraint on a decimal fixed point subtype with a given
delta, if it does not have a range_constraint, then it specifies an implicit
range �(10**D�1)*delta .. +(10**D�1)*delta, where D is the value of the
expression. A digits_constraint is compatible
 with a decimal fixed point subtype if the value of the expression is no
greater than the digits of the subtype, and if it specifies (explicitly or
implicitly) a range that is compatible with the subtype.

19 The elaboration of a digits_constraint consists of the elaboration of the
range_constraint, if any. If a range_constraint is given, a check is made
that the bounds of the range are both in the range �(10**D�1)*delta ..
+(10**D�1)*delta, where D is the value of the (static) expression given
after the reserved word digits. If this check fails, Constraint_Error is
raised.

Implementation Requirements

20 The implementation shall support at least 24 bits of precision (including
the sign bit) for fixed point types.

Implementation Permissions

21 Implementations are permitted to support only smalls that are a power of
two. In particular, all decimal fixed point type declarations can be
disallowed. Note however that conformance with the Information Systems Annex
requires support for decimal smalls, and decimal fixed point type
declarations with digits up to at least 18.

NOTES

22 36 The base range of an ordinary fixed point type need not include the
specified bounds themselves so that the range specification can be given in
a natural way, such as:

23 type Fraction is delta 2.0**(�15) range �1.0 .. 1.0;

24 With 2�s complement hardware, such a type could have a signed 16-bit
representation, using 1 bit for the sign and 15 bits for fraction, resulting
in a base range of �1.0 .. 1.0�2.0**(�15).

Examples

25 Examples of fixed point types and subtypes:

26 type Volt is delta 0.125 range 0.0 .. 255.0;
27 -- A pure fraction which requires all the available
-- space in a word can be declared as the type Fraction:
type Fraction is delta System.Fine_Delta range �1.0 .. 1.0;
-- Fraction�Last = 1.0 � System.Fine_Delta
28 type Money is delta 0.01 digits 15;  -- decimal fixed point
subtype Salary is Money digits 10;
-- Money�Last = 10.0**13 � 0.01, Salary�Last = 10.0**8 � 0.01

Re: delta?

[Matthew Heaney]

ycli6@se.cuhk.edu.hk (yukchi) writes:

> what is the meaning of delta and digits in the following sentence?
> type Money is delta 0.01 digits 15;

This is the declaration of a decimal fixed point type.  It means values
of Money as small as 1 cent are exactly representable.  Compare this to
a floating point type, which can only approximate the value of 1 cent.

You could do something like that using just plain fixed point types,
like this:


  Money_Delta : constant := 0.01;

  Money_First : constant := Integer'Pos (Integer'First) * Money_Delta;

  Money_Last : constant := Integer'Pos (Integer'Last) * Money_Delta;

  type Money is delta Money_Delta range Money_First .. Money_Last;

  for Money'Small use Money_Delta;


which gives you the range you can fit in an object with the same
precision as Integer.

BTW: The attribute T'Pos is handy here, because it allows you to convert
a static subtype to a univeral type, which you can then use in a
universal expression.

delta?

[yukchi]

hihi
what is the meaning of delta and digits in the following sentence?
type Money is delta 0.01 digits 15;
thanks in advance!

yuk

Re: delta?

[Tom Moran]

>what is the meaning of delta and digits in the following sentence?
>type Money is delta 0.01 digits 15;
It means variables of type Money are exactly represented down to 0.01,
differences between such variables can be as small as 0.01, and the
variables can take a value as big as 15 decimal digits.  Given
  Dollars : Money;
Then Dollars can be as big as $9,999,999,999,999.99  and accurately
represent an amount down to the penny.