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Editorial changes: minor improvements to "Advanced Ada" course #1284

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Editorial change: correcting project name in code examples
gusthoff Oct 31, 2025
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Editorial change: correcting project name in code examples
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Editorial change: moving code to Custom_Floating_Point_Types package
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Adding small note on size of base types
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67 changes: 34 additions & 33 deletions content/courses/advanced-ada/parts/data_types/numeric_attributes.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -24,7 +24,7 @@ universal integer value. Let's get the modulus of the 32-bit :ada:`Modular`
type that we've declared in the :ada:`Num_Types` package of the previous
chapter:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Modular_1
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Modular_1

package Num_Types is

Expand All @@ -43,7 +43,8 @@ chapter:
Put_Line (Modulus_Value'Image);
end Show_Modular;

When we run this example, we get 4294967296, which is equal to :ada:`2**32`.
When we run this example, we get 4,294,967,296 |mdash| which is equal to
:ada:`2**32`.

:ada:`Mod` Attribute
~~~~~~~~~~~~~~~~~~~~
Expand All @@ -69,7 +70,7 @@ be something like :ada:`-2**31 .. 2**31 - 1`. (Note: we discussed the
Operations on modular integers use modular (wraparound) arithmetic. For
example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Modular_1
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Modular_1

with Ada.Text_IO; use Ada.Text_IO;

Expand All @@ -94,7 +95,7 @@ wrap around)? The answer in Ada is the former |mdash| that is, if you try to
convert, say, :ada:`Integer'(-1)` to :ada:`Modular`, you will get
:ada:`Constraint_Error`:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Modular_1
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Modular_1
:class: ada-run-expect-failure

with Ada.Text_IO; use Ada.Text_IO;
Expand All @@ -111,7 +112,7 @@ convert, say, :ada:`Integer'(-1)` to :ada:`Modular`, you will get

To solve this problem, we can use the :ada:`Mod` attribute:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Modular_1
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Modular_1

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -140,7 +141,7 @@ given modular type, using wraparound semantics.
The :ada:`Mod` attribute was added to Ada 2005 to solve this problem.
Also, we can now safely use this attribute in generics. For example:

.. code:: ada compile_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Mod_Attribute
.. code:: ada compile_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Mod_Attribute

generic
type Formal_Modular is mod <>;
Expand Down Expand Up @@ -180,7 +181,7 @@ performed.

Let's see a simple implementation of the CRC-CCITT (0x1D0F) algorithm:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Modular_Types.Mod_Crc_CCITT_Ada
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Modular_Types.Mod_Crc_CCITT_Ada

package Crc_Defs is

Expand Down Expand Up @@ -298,7 +299,7 @@ Attribute: :ada:`Machine_Radix`
:ada:`Machine_Radix` is an attribute that returns the radix of the hardware
representation of a type. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Machine_Radix
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Machine_Radix

with Ada.Text_IO; use Ada.Text_IO;

Expand All @@ -324,7 +325,7 @@ Attributes: :ada:`Machine_Mantissa`
:ada:`Machine_Mantissa` is an attribute that returns the number of bits
reserved for the mantissa of the floating-point type. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Machine_Mantissa
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Machine_Mantissa

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -352,7 +353,7 @@ and maximum value, respectively, of the machine exponent the floating-point
type. Note that, in all cases, the returned value is a universal integer. For
example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Machine_Emin_Emax
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Machine_Emin_Emax

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -405,7 +406,7 @@ Attribute: :ada:`Digits`
:ada:`Digits` is an attribute that returns the requested decimal precision of
a floating-point subtype. Let's see an example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Digits
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Digits

with Ada.Text_IO; use Ada.Text_IO;

Expand All @@ -425,7 +426,7 @@ Note that we said that :ada:`Digits` is the *requested* level of precision,
which is specified as part of declaring a floating point type. We can retrieve
the actual decimal precision with :ada:`Base'Digits`. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Base_Digits
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Base_Digits

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -462,7 +463,7 @@ indicating whether a feature is available or not in the target architecture:
:ada:`Constraint_Error` exception is (or is not) guaranteed to be raised
when an operation with that type produces an overflow or divide-by-zero.

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Machine_Rounds_Overflows
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Machine_Rounds_Overflows

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -541,7 +542,7 @@ floating-point value:

Let's see some examples:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Exponent_Fraction
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Exponent_Fraction

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -600,7 +601,7 @@ Attribute: :ada:`Scaling`
:ada:`Scaling` is an attribute that scales a floating-point value based on the
machine radix and a machine exponent passed to the function. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Scaling
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Scaling

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -629,7 +630,7 @@ Round-up and round-down attributes
:ada:`Floor` and :ada:`Ceiling` are attributes that returned the rounded-down
or rounded-up value, respectively, of a floating-point value. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Floor_Ceiling
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Floor_Ceiling

with Ada.Text_IO; use Ada.Text_IO;

Expand All @@ -655,7 +656,7 @@ is the closest integer value.

Let's see a code example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Rounding
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Rounding

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -752,7 +753,7 @@ second parameter is the :ada:`Towards` value.

Let's see a code example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Truncation_Remainder
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Truncation_Remainder

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -837,7 +838,7 @@ mantissa. Let's see some examples:

Let's see some examples:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Sign_Leading
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Sign_Leading

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -879,7 +880,7 @@ Not every real number is directly representable as a floating-point value on a
specific machine. For example, let's take a value such as 1.0 x 10\ :sup:`15`
(or 1,000,000,000,000,000):

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Float_Value
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Float_Value

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -932,7 +933,7 @@ the difference between the original real value in our example
(1.0 x 10\ :sup:`15`) and the actual value that is assigned to :ada:`V`. We can
do this by using the :ada:`Machine` attribute in the calculation:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Machine_Attribute
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Machine_Attribute

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1028,7 +1029,7 @@ This is the reason why we see 1.3008896 x 10\ :sup:`7` instead of

Let's see an example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Model_Mantissa
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Model_Mantissa

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1075,7 +1076,7 @@ This is the reason why we see 1.3008896 x 10\ :sup:`7` instead of

Let's see some examples:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Model_Epsilon_Small
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Model_Epsilon_Small

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1118,7 +1119,7 @@ This is the reason why we see 1.3008896 x 10\ :sup:`7` instead of
value in 1.0 x 10\ :sup:`15` and the actual model value, we can use the
:ada:`Model` attribute:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Model_Attribute
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Model_Attribute

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1169,7 +1170,7 @@ This is the reason why we see 1.3008896 x 10\ :sup:`7` instead of
Let's see a code example with these attributes and compare them to the
:ada:`First` and :ada:`Last` attributes:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Safe_First_Last
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Floating_Point_Types.Safe_First_Last

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1229,7 +1230,7 @@ Attribute: :ada:`Machine_Radix`
:ada:`Machine_Radix` is an attribute that returns the radix of the hardware
representation of a type. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Fixed_Machine_Radix
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Fixed_Machine_Radix

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1265,7 +1266,7 @@ indicating whether a feature is available or not in the target architecture:
:ada:`Constraint_Error` is guaranteed to be raised when a fixed-point
operation with that type produces an overflow or divide-by-zero.

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Fixed_Machine_Rounds_Overflows
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Fixed_Machine_Rounds_Overflows

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1314,7 +1315,7 @@ it's automatically selected by the compiler, and it's always equal to the

Let's see an example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Fixed_Small_Delta
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Fixed_Small_Delta

package Fixed_Small_Delta is
D3 : constant := 10.0 ** (-3);
Expand Down Expand Up @@ -1386,7 +1387,7 @@ In the case of the :ada:`TQ15` type, we're specifying the *small* by using the
type is 32 bits, while the precision we get when operating with this type is
16 bits. Let's see a specific example for this type:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Fixed_Small_Delta
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Fixed_Small_Delta

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1431,7 +1432,7 @@ precise:

Let's see an example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Fixed_Fore_Aft
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Fixed_Fore_Aft

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1485,7 +1486,7 @@ use for the :ada:`digits` in the definition of a decimal fixed-point type.

Let's see an example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Decimal_Digits
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Decimal_Digits

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1527,7 +1528,7 @@ of :ada:`T'Scale` is three.

Let's look at this complete example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Decimal_Scale
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Decimal_Scale

with Ada.Text_IO; use Ada.Text_IO;

Expand Down Expand Up @@ -1570,7 +1571,7 @@ value, while the returned value is of :ada:`S'Base` type.

Let's look at this example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Fixed_Point_Types.Decimal_Round
.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numeric_Attributes.Fixed_Point_Types.Decimal_Round

with Ada.Text_IO; use Ada.Text_IO;

Expand Down
32 changes: 23 additions & 9 deletions content/courses/advanced-ada/parts/data_types/numerics.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -785,7 +785,7 @@ In this example, we get a compilation error because the range of the
.. admonition:: For further reading...

To circumvent the compilation error in the code example we've just seen,
the best alternative to use :ref:`big numbers <Adv_Ada_Big_Numbers>`
the best alternative is to use :ref:`big numbers <Adv_Ada_Big_Numbers>`
|mdash| we discuss this topic later on in this chapter:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Universal_Numeric_Types.Conversion_To_Non_Universal_Types switches=Compiler(-gnat2022);
Expand Down Expand Up @@ -2315,7 +2315,7 @@ As expected, we can derive from any floating-point type. For example:
with Ada.Text_IO; use Ada.Text_IO;

with Custom_Floating_Point_Types;
use Custom_Floating_Point_Types;
use Custom_Floating_Point_Types;

procedure Show_Derived_Floating_Point_Types is
C : Coefficient;
Expand Down Expand Up @@ -2463,9 +2463,7 @@ still select a 32-bit floating-point type for the target platform. For example:

.. code:: ada run_button project=Courses.Advanced_Ada.Data_Types.Numerics.Floating_Point_Types.Floating_Point_Decimal_Precision

with Ada.Text_IO; use Ada.Text_IO;

procedure Show_Decimal_Digits is
package Custom_Floating_Point_Types is

type Float_1_Digits is
digits 1;
Expand Down Expand Up @@ -2503,6 +2501,15 @@ still select a 32-bit floating-point type for the target platform. For example:
digits 17;
type Float_18_Digits is
digits 18;

end Custom_Floating_Point_Types;

with Ada.Text_IO; use Ada.Text_IO;

with Custom_Floating_Point_Types;
use Custom_Floating_Point_Types;

procedure Show_Decimal_Digits is
begin
Put_Line ("Float_1_Digits'Size :"
& Float_1_Digits'Size'Image
Expand Down Expand Up @@ -2577,6 +2584,10 @@ floating-point data types on the target hardware. However, as you might recall
from an earlier chapter, we can request specific sizes for custom types. We
discuss this topic next.

Note that, for the example above, the size of the type is equal to the size of
its base type, i.e. :ada:`Float_1_Digits'Size = Float_1_Digits'Base'Size`,
:ada:`Float_2_Digits'Size = Float_2_Digits'Base'Size`, and so on.


.. _Adv_Ada_Floating_Point_Type_Size:

Expand Down Expand Up @@ -2613,6 +2624,9 @@ bits to be represented |mdash| instead of the 32 bits that we would typically
see on a desktop PC. (Also, remember that this code example won't compile if
your target architecture doesn't support 128-bit floating-point data types.)

.. todo::

Discuss :ada:`Float_6_Digits'Size` vs. :ada:`Float_6_Digits'Base'Size`.


Range of custom floating-point types and subtypes
Expand Down Expand Up @@ -3363,7 +3377,7 @@ it's always equal to the *delta*.
For example, we may define a normalized range between -1.0 and 1.0 as
following:

.. code:: ada run_button project=Courses.Intro_To_Ada.Fixed_Point_Types.Normalized_Fixed_Point_Type
.. code:: ada run_button project=Courses.Advanced_Ada.Fixed_Point_Types.Normalized_Fixed_Point_Type

with Ada.Text_IO; use Ada.Text_IO;

Expand All @@ -3390,7 +3404,7 @@ it's always equal to the *delta*.

We may also rewrite this code with an exact type definition:

.. code:: ada compile_button project=Courses.Intro_To_Ada.Fixed_Point_Types.Normalized_Adapted_Fixed_Point_Type
.. code:: ada compile_button project=Courses.Advanced_Ada.Fixed_Point_Types.Normalized_Adapted_Fixed_Point_Type

procedure Normalized_Adapted_Fixed_Point_Type is
type TQ31 is
Expand All @@ -3402,7 +3416,7 @@ it's always equal to the *delta*.

We may also use any other range. For example:

.. code:: ada run_button project=Courses.Intro_To_Ada.Fixed_Point_Types.Custom_Fixed_Point_Range
.. code:: ada run_button project=Courses.Advanced_Ada.Fixed_Point_Types.Custom_Fixed_Point_Range

with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics; use Ada.Numerics;
Expand Down Expand Up @@ -3431,7 +3445,7 @@ it's always equal to the *delta*.

All standard operations are available for fixed-point types. For example:

.. code:: ada run_button project=Courses.Intro_To_Ada.Fixed_Point_Types.Fixed_Point_Op
.. code:: ada run_button project=Courses.Advanced_Ada.Fixed_Point_Types.Fixed_Point_Op

with Ada.Text_IO; use Ada.Text_IO;

Expand Down
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