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