⟦f40852aad⟧

E3 Source Code



with Xlbt_Arithmetic;  
use Xlbt_Arithmetic;

package Trig is
------------------------------------------------------------------------------
-- Date      - /Name/ Comment
--
-- 01-FEB-89 - /GEB/ Created.
-- 27-FEB-89 - /GEB/ Add Float Decomposition routines.
-- 05-JUL-90 - /GEB/ Add structured comments, port to TeleGen2/TeleSoft.
------------------------------------------------------------------------------

    subtype Integer32  is S_Long;  
    subtype Natural32  is S_Natural;  
    subtype Positive32 is S_Positive;

----Useful constants.

    Pi        : constant Float :=  
       3.1415926535897932384626433832795028841971693993750990044278398981733785;  
    Two_Pi    : constant Float := Pi + Pi;  
    Pi_Over_2 : constant Float := Pi / 2.0;  
    Pi_Over_4 : constant Float := Pi / 4.0;  
    E         : constant Float :=  
       2.7182818284590452353602874713526624977572470936999595749669676277240766;

----Float/Integer32 conversions

    function Truncate (X : Float) return Float;
    ----Truncates the floating-point value.  Returns just the integral portion
    --  of the value.  abs Truncate(X) <= abs X.

    function Truncate (X : Float) return Integer32;
    ----Truncates the floating-point value.  Returns just the integral portion
    --  of the value.  abs Truncate(X) <= abs X.
    --  Note: Numeric_Error will be raised unless X is in the range
    --  Integer32'First..Integer32'Last.

    function Round (X : Float) return Float;
    ----Rounds the floating-point value so that it contains no fractional part.
    --  Functionally identical to the expression Float(Integer32(X)) except that
    --  Numeric_Error is not possible.
    --  abs Truncate(X) <= abs Round(X) <= abs Truncate(X)+1.0.

    function Round (X : Float) return Integer32;
    ----Functionally identical with the expression Integer32(X).  The
    --  floating-point value is rounded so that it contains no fractional part.

----Float Decomposition

    procedure Fraction_Exponent (X        :     Float;  
                                 Fraction : out Float;  
                                 Exponent : out Integer32);
    ----Returns both the fraction and the exponent of the Float.
    --  Fraction in 0.0..1.0/float(Float'Machine_Radix)
    --  Exponent in Float'Machine_Emin..Float'Machine_Emax

    function Odd (X : Float) return Boolean;
    ----Returns TRUE if Aint(X) is an ODD value.  Any value < 1.0 is even
    --  because it is less than 1;
    --  and any value > Float'Machine_Radix ** Float'Machine_Mantissa is
    --  even because the even/odd bit has been lost due to insufficient
    --  precision in the Float representation.

----Square-Root - returns the positive root of positive numbers
--              - raises Constraint_Error for negative numbers

    function Sqrt (A : Float) return Float;

----Cube-Root   - returns the real root

    function Cbrt (A : Float) return Float;

----In_Radians - Set this to TRUE to cause the trigonometric functions to work
--  in Radians and FALSE to cause them to work in degrees.

    In_Radians : Boolean := True;

----Sin - returns the sine of its argument
--  Cos - returns the cosine of its argument
--  Tan - returns the tangent of its argument

    function Sin (A : Float) return Float;  
    function Cos (A : Float) return Float;  
    function Tan (A : Float) return Float;

----Sec - returns the secant of its argument
--  Csc - returns the cosecant of its argument
--  Cot - returns the cotangent of its argument

    function Sec (A : Float) return Float;  
    function Csc (A : Float) return Float;  
    function Cot (A : Float) return Float;

----Asin - returns the inverse sine of its argument
--  Acos - returns the inverse cosine of its argument
--  Atan - returns the inverse tangent of its argument

    function Asin (A : Float) return Float;  
    function Acos (A : Float) return Float;  
    function Atan (A : Float) return Float;

----Asec - returns the inverse secant of its argument
--  Acsc - returns the inverse cosecant of its argument
--  Acot - returns the inverse cotangent of its argument

    function Asec (A : Float) return Float;  
    function Acsc (A : Float) return Float;  
    function Acot (A : Float) return Float;

----Ln  - returns the natural logarithm of its positive argument
--  Exp - returns E to the power represented by its argument

    function Ln  (A : Float) return Float;  
    function Exp (A : Float) return Float;

----Log10 - returns log-base-10 of its positive argument
--  Exp10 - returns 10 to the power represented by its argument

    function Log10 (A : Float) return Float;  
    function Exp10 (A : Float) return Float;

----Logx - returns log-base-X of its positive argument Y
--  Expx - returns X ** Y;
--          X ** 0.0 = 1.0;
--          X ** Y where X < 0.0 raises Constraint_Error

    fuction Logx (X : Float; Y : Float) return Float;  
    function Expx (X : Float; Y : Float) return Float;

----Sinh - returns the hyperbolic sine of its argument
--  Cosh - returns the hyperbolic cosine of its argument
--  Tanh - returns the hyperbolic tangent of its argument

    function Sinh (A : Float) return Float;  
    function Cosh (A : Float) return Float;  
    function Tanh (A : Float) return Float;

----Sech - returns the hyperbolic secant of its argument
--  Csch - returns the hyperbolic cosecant of its argument
--  Coth - returns the hyperbolic cotangent of its argument

    function Sech (A : Float) return Float;  
    function Csch (A : Float) return Float;  
    function Coth (A : Float) return Float;

----Asinh - returns the inverse hyperbolic sine of its argument
--  Acosh - returns the inverse hyperbolic cosine of its argument
--  Atanh - returns the inverse hyperbolic tangent of its argument

    function Asinh (A : Float) return Float;  
    function Acosh (A : Float) return Float;  
    function Atanh (A : Float) return Float;

----Asech - returns the inverse hyperbolic secant of its argument
--  Acsch - returns the inverse hyperbolic cosecant of its argument
--  Acoth - returns the inverse hyperbolic cotangent of its argument

    function Asech (A : Float) return Float;  
    function Acsch (A : Float) return Float;  
    function Acoth (A : Float) return Float;

end Trig;
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