Appendix F: Specifications of the Ada Math Libraries

This appendix, adapted from the Ada 95 Reference Manual, Sections A.5.1 and A.5.2, give the specifications for the packages Ada.Numerics, Ada.Numerics.Elementary_Functions, and Ada.Numerics.Float_Random, and the generic package Ada.Numerics.Discrete_Random,.
PACKAGE Ada.Numerics IS

  Argument_Error : EXCEPTION;
  Pi : CONSTANT :=
    3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37511;
  e  : CONSTANT :=
    2.71828_18284_59045_23536_02874_71352_66249_77572_47093_69996;

END Ada.Numerics;


PACKAGE Ada.Numerics.Elementary_Functions IS

  FUNCTION Sqrt    ( X           : Float)        RETURN Float;
  FUNCTION Log     ( X           : Float)        RETURN Float;
  FUNCTION Log     ( X, Base     : Float)        RETURN Float;
  FUNCTION Exp     ( X           : Float)        RETURN Float;
  FUNCTION "**"    ( Left, Right : Float)        RETURN Float;

  FUNCTION Sin     ( X           : Float)        RETURN Float;
  FUNCTION Sin     ( X, Cycle    : Float)        RETURN Float;
  FUNCTION Cos     ( X           : Float)        RETURN Float;
  FUNCTION Cos     ( X, Cycle    : Float)        RETURN Float;
  FUNCTION Tan     ( X           : Float)        RETURN Float;
  FUNCTION Tan     ( X, Cycle    : Float)        RETURN Float;
  FUNCTION Cot     ( X           : Float)        RETURN Float;
  FUNCTION Cot     ( X, Cycle    : Float)        RETURN Float;

  FUNCTION Arcsin  ( X           : Float)        RETURN Float;
  FUNCTION Arcsin  ( X, Cycle    : Float)        RETURN Float;
  FUNCTION Arccos  ( X           : Float)        RETURN Float;
  FUNCTION Arccos  ( X, Cycle    : Float)        RETURN Float;
  FUNCTION Arctan  ( Y           : Float;
                     X           : Float :=  . ) RETURN Float;
  FUNCTION Arctan  ( Y           : Float;
                     X           : Float :=  . ;
                     Cycle       : Float)        RETURN Float;
  FUNCTION Arccot  ( X           : Float;
                     Y           : Float :=  . ) RETURN Float;
  FUNCTION Arccot  ( X           : Float;
                     Y           : Float :=  . ;
                     Cycle       : Float)        RETURN Float;

  FUNCTION Sinh    ( X           : Float)        RETURN Float;
  FUNCTION Cosh    ( X           : Float)        RETURN Float;
  FUNCTION Tanh    ( X           : Float)        RETURN Float;
  FUNCTION Coth    ( X           : Float)        RETURN Float;
  FUNCTION Arcsinh ( X           : Float)        RETURN Float;
  FUNCTION Arccosh ( X           : Float)        RETURN Float;
  FUNCTION Arctanh ( X           : Float)        RETURN Float;
  FUNCTION Arccoth ( X           : Float)        RETURN Float;

END Ada.Numerics.Elementary_Functions;


PACKAGE Ada.Numerics.Float_Random IS

  -- Basic facilities

  TYPE Generator IS limited private;
  SUBTYPE Uniformly_Distributed IS Float RANGE 0.0 .. 1.0;
  FUNCTION Random ( Gen : Generator) RETURN Uniformly_Distributed;

  PROCEDURE Reset ( Gen       : IN Generator;
                    Initiator : IN Integer);
  PROCEDURE Reset ( Gen       : IN Generator);

  -- Advanced facilities

  TYPE State IS private;

  PROCEDURE Save  ( Gen        : IN  Generator;
                    To_State   : OUT State);
  PROCEDURE Reset ( Gen        : IN  Generator;
                    From_State : IN  State);

  Max_Image_Width : constant := implementation-defined integer value;

  FUNCTION Image ( Of_State    : State)  RETURN String;
  FUNCTION Value ( Coded_State : String) RETURN State;

PRIVATE
  ... -- not specified by the language
END Ada.Numerics.Float_Random;


GENERIC
  TYPE Result_SubTYPE IS (<>);
PACKAGE Ada.Numerics.Discrete_Random IS

  -- Basic facilities

  TYPE Generator IS limited private;

  FUNCTION Random ( Gen : Generator) RETURN Result_SubTYPE;

  PROCEDURE Reset ( Gen       : IN Generator;
                    Initiator : IN Integer);
  PROCEDURE Reset ( Gen       : IN Generator);

  -- Advanced facilities

  TYPE State IS private;

  PROCEDURE Save  ( Gen        : IN  Generator;
                    To_State   : OUT State);
  PROCEDURE Reset ( Gen        : IN  Generator;
                    From_State : IN  State);

  Max_Image_Width : constant := implementation-defined integer value;

  FUNCTION Image ( Of_State    : State)  RETURN String;
  FUNCTION Value ( Coded_State : String) RETURN State;

PRIVATE
  ... -- not specified by the language
END Ada.Numerics.Discrete_Random;