3.5.10 Operations of Fixed Point Types

1. The following attributes are defined for every fixed point subtype S:
2. S'Small

   S'Small denotes the small of the type of S. The value of
   this attribute is of the type universal_real. Small may
   be specified for nonderived fixed point types via an
   attribute_definition_clause, See section 13.3 Representation Attributes; the expression
   of such a clause shall be static.
   

3. S'Delta

   S'Delta denotes the delta of the fixed point subtype S. The
   value of this attribute is of the type universal_real.
   

4. S'Fore

   S'Fore yields the minimum number of characters needed
   before the decimal point for the decimal representation
   of any value of the subtype S, assuming that the
   representation does not include an exponent, but
   includes a one-character prefix that is either a minus
   sign or a space. (This minimum number does not include
   superfluous zeros or underlines, and is at least 2.) The
   value of this attribute is of the type
   universal_integer.
   

5. S'Aft

   S'Aft yields the number of decimal digits needed after the
   decimal point to accommodate the delta of the subtype S,
   unless the delta of the subtype S is greater than 0.1, in
   which case the attribute yields the value one. (S'Aft is the
   smallest positive integer N for which (10**N)*S'Delta is
   greater than or equal to one.) The value of this attribute
   is of the type universal_integer.
   

6. The following additional attributes are defined for every decimal fixed point subtype S:
7. S'Digits

   S'Digits denotes the digits of the decimal fixed point
   subtype S, which corresponds to the number of decimal digits
   that are representable in objects of the subtype. The value
   of this attribute is of the type universal_integer. Its
   value is determined as follows:
   

   1. For a first subtype or a subtype defined by a subtype_indication with a digits_constraint, the digits is the value of the expression given after the reserved word digits;
   2. For a subtype defined by a subtype_indication without a digits_constraint, the digits of the subtype is the same as that of the subtype denoted by the subtype_mark in the subtype_indication.
   3. The digits of a base subtype is the largest integer D such that the range -(10**D-1)*delta .. +(10**D-1)*delta is included in the base range of the type.

1. S'Scale

   S'Scale denotes the scale of the subtype S, defined as the
   value N such that S'Delta = 10.0**(-N). The scale indicates
   the position of the point relative to the rightmost
   significant digits of values of subtype S. The value of this
   attribute is of the type universal_integer.
   

2. S'Round
   S'Round denotes a function with the following specification:

   1. function S'Round(X : universal_real)
        return S'Base
      

   2. The function returns the value obtained by rounding X (away from 0, if X is midway between two values of the type of S).

NOTES


1. (37) All subtypes of a fixed point type will have the same value for the Delta attribute, in the absence of delta_constraints, See section J.3 Reduced Accuracy Subtypes.
2. (38) S'Scale is not always the same as S'Aft for a decimal subtype; for example, if S'Delta = 1.0 then S'Aft is 1 while S'Scale is 0.
3. (39) The predefined operations of a fixed point type include the assignment operation, qualification, the membership tests, and explicit conversion to and from other numeric types. They also include the relational operators and the following predefined arithmetic operators: the binary and unary adding operators - and +, multiplying operators, and the unary operator abs.
4. (40) As for all types, objects of a fixed point type have Size and Address attributes, See section 13.3 Representation Attributes. Other attributes of fixed point types are defined in See section A.5.4 Attributes of Fixed Point Types.

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