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328 | with
ada.Numerics.generic_elementary_Functions,
ada.Numerics.generic_complex_Types,
ada.Numerics.generic_real_Arrays,
ada.Containers;
generic
type Real_t is digits <>;
package any_Math
--
-- Provides math for any given floating point type.
--
is
pragma Pure;
----------
-- Indices
--
subtype Index is standard.Integer;
type Indices is array (Index range <>) of Index;
-----------
-- Counters
--
subtype Counter is ada.Containers.Count_Type;
procedure increment (Self : in out Counter; By : in Counter := 1);
procedure decrement (Self : in out Counter; By : in Counter := 1);
-----------
-- Integers
--
procedure increment (Self : in out Integer; By : in Integer := 1);
procedure decrement (Self : in out Integer; By : in Integer := 1);
procedure swap (Left, Right : in out Integer);
type Integers is array (Index range <>) of aliased Integer;
type Naturals is array (Index range <>) of aliased Natural;
type Positives is array (Index range <>) of aliased Positive;
--------
-- Reals
--
subtype Real is Real_t;
subtype unit_Interval is Real range 0.0 .. 1.0;
function almost_Zero (Self : in Real) return Boolean;
function Clamped (Self : in Real; Low, High : in Real) return Real;
procedure clamp (Self : in out Real; Low, High : in Real);
procedure swap (Left,
Right : in out Real);
function Image (Self : in Real; Precision : in Natural := 5) return String;
-------------
-- Percentage
--
type Percentage is new Real;
subtype unit_Percentage is Percentage range 0.0 .. 100.0;
function to_Percentage (From : in Real) return Percentage;
function to_Real (Percent : in Percentage) return Real;
function Image (Percent : in Percentage;
Precision : in Natural := 5) return String;
function apply (Percent : in Percentage;
To : in Real) return Real;
function apply (Left,
Right : in Percentage) return Percentage;
------------
-- Functions
--
package Functions is new ada.Numerics.generic_elementary_Functions (Real);
------------------
-- Complex Numbers
--
package complex_Reals is new ada.Numerics.generic_complex_Types (Real);
---------
-- Angles
--
subtype Radians is Real;
type Degrees is new Real;
function to_Radians (Self : in Degrees) return Radians;
function to_Degrees (Self : in Radians) return Degrees;
----------
-- Vectors
--
package Vectors is new ada.Numerics.generic_real_Arrays (Real'Base);
subtype Vector is Vectors.real_Vector;
function Sum (Self : in Vector) return Real;
function Average (Self : in Vector) return Real;
function Max (Self : in Vector) return Real;
function Min (Self : in Vector) return Real;
function Image (Self : in Vector; Precision : in Natural := 5) return String;
type Vector_1 is new Vector (1 .. 1);
type Vector_2 is new Vector (1 .. 2);
type Vector_3 is new Vector (1 .. 3);
type Vector_4 is new Vector (1 .. 4);
type Vector_8 is new Vector (1 .. 8);
type Vector_12 is new Vector (1 .. 12);
type Vector_16 is new Vector (1 .. 16);
-----------
-- Vector_2
--
function to_Vector_2 (Self : in Vector_3) return Vector_2;
function Image (Self : in Vector_2; Precision : in Natural := 5) return String;
overriding
function "+" (Left, Right : in Vector_2) return Vector_2;
overriding
function "-" (Left, Right : in Vector_2) return Vector_2;
overriding
function "*" (Left : in Real; Right : in Vector_2) return Vector_2;
overriding
function "*" (Left : in Vector_2; Right : in Real) return Vector_2;
overriding
function "/" (Left : in Vector_2; Right : in Real) return Vector_2;
-----------
-- Vector_3
--
function to_Vector_3 (Self : in Vector_2; Z : in Real := 0.0) return Vector_3;
function Image (Self : in Vector_3; Precision : in Natural := 5) return String;
overriding
function "*" (Left : in Real; Right : in Vector_3) return Vector_3;
overriding
function "*" (Left : in Vector_3; Right : in Real) return Vector_3;
function "*" (Left, Right : in Vector_3) return Vector_3; -- Cross product.
overriding
function "+" (Left, Right : in Vector_3) return Vector_3;
overriding
function "-" (Left, Right : in Vector_3) return Vector_3;
overriding
function "-" (Right : in Vector_3) return Vector_3;
overriding
function "/" (Left : in Vector_3; Right : in Real) return Vector_3;
overriding
function "abs" (Right : in Vector_3) return Vector_3;
-----------
-- Matrices
--
-- Memory layout is row-major.
subtype Matrix is Vectors.real_Matrix;
type Matrix_2x2 is new Matrix (1 .. 2, 1 .. 2);
type Matrix_3x3 is new Matrix (1 .. 3, 1 .. 3);
type Matrix_4x4 is new Matrix (1 .. 4, 1 .. 4);
Identity_2x2 : aliased constant Matrix_2x2;
Identity_3x3 : constant Matrix_3x3;
Identity_4x4 : constant Matrix_4x4;
function Image (Self : in Matrix) return String;
-------------
-- Matrix_2x2
--
overriding
function Transpose (Self : in Matrix_2x2) return Matrix_2x2;
function "*" (Left : in Vector_2; Right : in Matrix_2x2) return Vector_2;
function "*" (Left : in Matrix_2x2; Right : in Vector_2) return Vector_2;
function Row (Self : in Matrix_2x2; row_Id : in Index) return Vector_2;
function Col (Self : in Matrix_2x2; col_Id : in Index) return Vector_2;
-------------
-- Matrix_3x3
--
overriding
function Transpose (Self : in Matrix_3x3) return Matrix_3x3;
function "*" (Left : in Vector_3; Right : in Matrix_3x3) return Vector_3;
function "*" (Left : in Matrix_3x3; Right : in Vector_3) return Vector_3;
function Row (Self : in Matrix_3x3; row_Id : in Index) return Vector_3;
function Col (Self : in Matrix_3x3; col_Id : in Index) return Vector_3;
-------------
-- Matrix_4x4
--
overriding
function Transpose (Self : in Matrix_4x4) return Matrix_4x4;
function "*" (Left : in Vector_4; Right : in Matrix_4x4) return Vector_4;
function "*" (Left : in Matrix_4x4; Right : in Vector_4) return Vector_4;
function "*" (Left : in Matrix_4x4; Right : in Vector_3) return Vector_3;
function "*" (Left : in Vector_3; Right : in Matrix_4x4) return Vector_4;
function "*" (Left : in Matrix_4x4; Right : in Vector_3) return Vector_4;
overriding
function "*" (Left : in Matrix_4x4; Right : in Matrix_4x4) return Matrix_4x4;
function Row (Self : in Matrix_4x4; row_Id : in Index) return Vector_4;
function Col (Self : in Matrix_4x4; col_Id : in Index) return Vector_4;
function to_Vector_16 (Self : in Matrix_4x4) return Vector_16;
function to_Matrix_4x4 (Self : in Vector_16) return Matrix_4x4;
--------------
-- Quaternions
--
type Quaternion is
record
R : Real; -- Scalar part.
V : Vector_3; -- Vector part.
end record;
function to_Quaternion (From : in Vector_4) return Quaternion;
function to_Vector (From : in Quaternion) return Vector_4;
function "*" (Left : in Quaternion; Right : in Real) return Quaternion;
function "*" (Left : in Real; Right : in Quaternion) return Quaternion;
function "/" (Left : in Quaternion; Right : in Real) return Quaternion;
function "+" (Left, Right : in Quaternion) return Quaternion;
function "-" (Left, Right : in Quaternion) return Quaternion;
function Image (Self : in Quaternion; Precision : in Natural := 5) return String;
-------------
-- Transforms
--
type Transform_2d is
record
Rotation : aliased Matrix_2x2;
Translation : aliased Vector_2;
end record;
type Transform_3d is
record
Rotation : aliased Matrix_3x3;
Translation : aliased Vector_3;
end record;
null_Transform_2d : constant Transform_2d; -- No translation and no rotation.
null_Transform_3d : constant Transform_3d; --
------------
-- Constants
--
Infinity : constant Real;
Pi : constant := ada.numerics.Pi;
Phi : constant := 1.6180339887_4989484820_4586834365_6381177203_0917980576_2862135448_6227052604_6281890244_9707207204_1893911374;
--
-- The 'Golden' ratio.
Origin_2D : constant Vector_2;
Origin_3D : constant Vector_3;
private
Infinity : constant Real := Real'Last;
Origin_2D : constant Vector_2 := (0.0, 0.0);
Origin_3D : constant Vector_3 := (0.0, 0.0, 0.0);
Identity_2x2 : aliased constant Matrix_2x2 := ((1.0, 0.0),
(0.0, 1.0));
Identity_3x3 : constant Matrix_3x3 := ((1.0, 0.0, 0.0),
(0.0, 1.0, 0.0),
(0.0, 0.0, 1.0));
Identity_4x4 : constant Matrix_4x4 := ((1.0, 0.0, 0.0, 0.0),
(0.0, 1.0, 0.0, 0.0),
(0.0, 0.0, 1.0, 0.0),
(0.0, 0.0, 0.0, 1.0));
null_Transform_2d : constant Transform_2d := (translation => (0.0, 0.0),
rotation => ((1.0, 0.0),
(0.0, 1.0)));
null_Transform_3d : constant Transform_3d := (translation => (0.0, 0.0, 0.0),
rotation => ((1.0, 0.0, 0.0),
(0.0, 1.0, 0.0),
(0.0, 0.0, 1.0)));
pragma Inline_Always (increment);
pragma Inline_Always (decrement);
pragma Inline_Always (Clamped);
end any_Math;
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