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------------------------------------------------------------------------------ -- -- -- GNAT RUN-TIME COMPONENTS -- -- -- -- A D A . N U M E R I C S . G E N E R I C _ C O M P L E X _ T Y P E S -- -- -- -- B o d y -- -- -- -- Copyright (C) 1992-2009, Free Software Foundation, Inc. -- -- -- -- GNAT is free software; you can redistribute it and/or modify it under -- -- terms of the GNU General Public License as published by the Free Soft- -- -- ware Foundation; either version 3, or (at your option) any later ver- -- -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- -- or FITNESS FOR A PARTICULAR PURPOSE. -- -- -- -- As a special exception under Section 7 of GPL version 3, you are granted -- -- additional permissions described in the GCC Runtime Library Exception, -- -- version 3.1, as published by the Free Software Foundation. -- -- -- -- You should have received a copy of the GNU General Public License and -- -- a copy of the GCC Runtime Library Exception along with this program; -- -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- -- <http://www.gnu.org/licenses/>. -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ with Ada.Numerics.Aux; use Ada.Numerics.Aux; package body Ada.Numerics.Generic_Complex_Types is subtype R is Real'Base; Two_Pi : constant R := R (2.0) * Pi; Half_Pi : constant R := Pi / R (2.0); --------- -- "*" -- --------- function "*" (Left, Right : Complex) return Complex is X : R; Y : R; begin X := Left.Re * Right.Re - Left.Im * Right.Im; Y := Left.Re * Right.Im + Left.Im * Right.Re; -- If either component overflows, try to scale (skip in fast math mode) if not Standard'Fast_Math then if abs (X) > R'Last then X := R'(4.0) * (R'(Left.Re / 2.0) * R'(Right.Re / 2.0) - R'(Left.Im / 2.0) * R'(Right.Im / 2.0)); end if; if abs (Y) > R'Last then Y := R'(4.0) * (R'(Left.Re / 2.0) * R'(Right.Im / 2.0) - R'(Left.Im / 2.0) * R'(Right.Re / 2.0)); end if; end if; return (X, Y); end "*"; function "*" (Left, Right : Imaginary) return Real'Base is begin return -(R (Left) * R (Right)); end "*"; function "*" (Left : Complex; Right : Real'Base) return Complex is begin return Complex'(Left.Re * Right, Left.Im * Right); end "*"; function "*" (Left : Real'Base; Right : Complex) return Complex is begin return (Left * Right.Re, Left * Right.Im); end "*"; function "*" (Left : Complex; Right : Imaginary) return Complex is begin return Complex'(-(Left.Im * R (Right)), Left.Re * R (Right)); end "*"; function "*" (Left : Imaginary; Right : Complex) return Complex is begin return Complex'(-(R (Left) * Right.Im), R (Left) * Right.Re); end "*"; function "*" (Left : Imaginary; Right : Real'Base) return Imaginary is begin return Left * Imaginary (Right); end "*"; function "*" (Left : Real'Base; Right : Imaginary) return Imaginary is begin return Imaginary (Left * R (Right)); end "*"; ---------- -- "**" -- ---------- function "**" (Left : Complex; Right : Integer) return Complex is Result : Complex := (1.0, 0.0); Factor : Complex := Left; Exp : Integer := Right; begin -- We use the standard logarithmic approach, Exp gets shifted right -- testing successive low order bits and Factor is the value of the -- base raised to the next power of 2. For positive exponents we -- multiply the result by this factor, for negative exponents, we -- divide by this factor. if Exp >= 0 then -- For a positive exponent, if we get a constraint error during -- this loop, it is an overflow, and the constraint error will -- simply be passed on to the caller. while Exp /= 0 loop if Exp rem 2 /= 0 then Result := Result * Factor; end if; Factor := Factor * Factor; Exp := Exp / 2; end loop; return Result; else -- Exp < 0 then -- For the negative exponent case, a constraint error during this -- calculation happens if Factor gets too large, and the proper -- response is to return 0.0, since what we essentially have is -- 1.0 / infinity, and the closest model number will be zero. begin while Exp /= 0 loop if Exp rem 2 /= 0 then Result := Result * Factor; end if; Factor := Factor * Factor; Exp := Exp / 2; end loop; return R'(1.0) / Result; exception when Constraint_Error => return (0.0, 0.0); end; end if; end "**"; function "**" (Left : Imaginary; Right : Integer) return Complex is M : constant R := R (Left) ** Right; begin case Right mod 4 is when 0 => return (M, 0.0); when 1 => return (0.0, M); when 2 => return (-M, 0.0); when 3 => return (0.0, -M); when others => raise Program_Error; end case; end "**"; --------- -- "+" -- --------- function "+" (Right : Complex) return Complex is begin return Right; end "+"; function "+" (Left, Right : Complex) return Complex is begin return Complex'(Left.Re + Right.Re, Left.Im + Right.Im); end "+"; function "+" (Right : Imaginary) return Imaginary is begin return Right; end "+"; function "+" (Left, Right : Imaginary) return Imaginary is begin return Imaginary (R (Left) + R (Right)); end "+"; function "+" (Left : Complex; Right : Real'Base) return Complex is begin return Complex'(Left.Re + Right, Left.Im); end "+"; function "+" (Left : Real'Base; Right : Complex) return Complex is begin return Complex'(Left + Right.Re, Right.Im); end "+"; function "+" (Left : Complex; Right : Imaginary) return Complex is begin return Complex'(Left.Re, Left.Im + R (Right)); end "+"; function "+" (Left : Imaginary; Right : Complex) return Complex is begin return Complex'(Right.Re, R (Left) + Right.Im); end "+"; function "+" (Left : Imaginary; Right : Real'Base) return Complex is begin return Complex'(Right, R (Left)); end "+"; function "+" (Left : Real'Base; Right : Imaginary) return Complex is begin return Complex'(Left, R (Right)); end "+"; --------- -- "-" -- --------- function "-" (Right : Complex) return Complex is begin return (-Right.Re, -Right.Im); end "-"; function "-" (Left, Right : Complex) return Complex is begin return (Left.Re - Right.Re, Left.Im - Right.Im); end "-"; function "-" (Right : Imaginary) return Imaginary is begin return Imaginary (-R (Right)); end "-"; function "-" (Left, Right : Imaginary) return Imaginary is begin return Imaginary (R (Left) - R (Right)); end "-"; function "-" (Left : Complex; Right : Real'Base) return Complex is begin return Complex'(Left.Re - Right, Left.Im); end "-"; function "-" (Left : Real'Base; Right : Complex) return Complex is begin return Complex'(Left - Right.Re, -Right.Im); end "-"; function "-" (Left : Complex; Right : Imaginary) return Complex is begin return Complex'(Left.Re, Left.Im - R (Right)); end "-"; function "-" (Left : Imaginary; Right : Complex) return Complex is begin return Complex'(-Right.Re, R (Left) - Right.Im); end "-"; function "-" (Left : Imaginary; Right : Real'Base) return Complex is begin return Complex'(-Right, R (Left)); end "-"; function "-" (Left : Real'Base; Right : Imaginary) return Complex is begin return Complex'(Left, -R (Right)); end "-"; --------- -- "/" -- --------- function "/" (Left, Right : Complex) return Complex is a : constant R := Left.Re; b : constant R := Left.Im; c : constant R := Right.Re; d : constant R := Right.Im; begin if c = 0.0 and then d = 0.0 then raise Constraint_Error; else return Complex'(Re => ((a * c) + (b * d)) / (c ** 2 + d ** 2), Im => ((b * c) - (a * d)) / (c ** 2 + d ** 2)); end if; end "/"; function "/" (Left, Right : Imaginary) return Real'Base is begin return R (Left) / R (Right); end "/"; function "/" (Left : Complex; Right : Real'Base) return Complex is begin return Complex'(Left.Re / Right, Left.Im / Right); end "/"; function "/" (Left : Real'Base; Right : Complex) return Complex is a : constant R := Left; c : constant R := Right.Re; d : constant R := Right.Im; begin return Complex'(Re => (a * c) / (c ** 2 + d ** 2), Im => -((a * d) / (c ** 2 + d ** 2))); end "/"; function "/" (Left : Complex; Right : Imaginary) return Complex is a : constant R := Left.Re; b : constant R := Left.Im; d : constant R := R (Right); begin return (b / d, -(a / d)); end "/"; function "/" (Left : Imaginary; Right : Complex) return Complex is b : constant R := R (Left); c : constant R := Right.Re; d : constant R := Right.Im; begin return (Re => b * d / (c ** 2 + d ** 2), Im => b * c / (c ** 2 + d ** 2)); end "/"; function "/" (Left : Imaginary; Right : Real'Base) return Imaginary is begin return Imaginary (R (Left) / Right); end "/"; function "/" (Left : Real'Base; Right : Imaginary) return Imaginary is begin return Imaginary (-(Left / R (Right))); end "/"; --------- -- "<" -- --------- function "<" (Left, Right : Imaginary) return Boolean is begin return R (Left) < R (Right); end "<"; ---------- -- "<=" -- ---------- function "<=" (Left, Right : Imaginary) return Boolean is begin return R (Left) <= R (Right); end "<="; --------- -- ">" -- --------- function ">" (Left, Right : Imaginary) return Boolean is begin return R (Left) > R (Right); end ">"; ---------- -- ">=" -- ---------- function ">=" (Left, Right : Imaginary) return Boolean is begin return R (Left) >= R (Right); end ">="; ----------- -- "abs" -- ----------- function "abs" (Right : Imaginary) return Real'Base is begin return abs R (Right); end "abs"; -------------- -- Argument -- -------------- function Argument (X : Complex) return Real'Base is a : constant R := X.Re; b : constant R := X.Im; arg : R; begin if b = 0.0 then if a >= 0.0 then return 0.0; else return R'Copy_Sign (Pi, b); end if; elsif a = 0.0 then if b >= 0.0 then return Half_Pi; else return -Half_Pi; end if; else arg := R (Atan (Double (abs (b / a)))); if a > 0.0 then if b > 0.0 then return arg; else -- b < 0.0 return -arg; end if; else -- a < 0.0 if b >= 0.0 then return Pi - arg; else -- b < 0.0 return -(Pi - arg); end if; end if; end if; exception when Constraint_Error => if b > 0.0 then return Half_Pi; else return -Half_Pi; end if; end Argument; function Argument (X : Complex; Cycle : Real'Base) return Real'Base is begin if Cycle > 0.0 then return Argument (X) * Cycle / Two_Pi; else raise Argument_Error; end if; end Argument; ---------------------------- -- Compose_From_Cartesian -- ---------------------------- function Compose_From_Cartesian (Re, Im : Real'Base) return Complex is begin return (Re, Im); end Compose_From_Cartesian; function Compose_From_Cartesian (Re : Real'Base) return Complex is begin return (Re, 0.0); end Compose_From_Cartesian; function Compose_From_Cartesian (Im : Imaginary) return Complex is begin return (0.0, R (Im)); end Compose_From_Cartesian; ------------------------ -- Compose_From_Polar -- ------------------------ function Compose_From_Polar ( Modulus, Argument : Real'Base) return Complex is begin if Modulus = 0.0 then return (0.0, 0.0); else return (Modulus * R (Cos (Double (Argument))), Modulus * R (Sin (Double (Argument)))); end if; end Compose_From_Polar; function Compose_From_Polar ( Modulus, Argument, Cycle : Real'Base) return Complex is Arg : Real'Base; begin if Modulus = 0.0 then return (0.0, 0.0); elsif Cycle > 0.0 then if Argument = 0.0 then return (Modulus, 0.0); elsif Argument = Cycle / 4.0 then return (0.0, Modulus); elsif Argument = Cycle / 2.0 then return (-Modulus, 0.0); elsif Argument = 3.0 * Cycle / R (4.0) then return (0.0, -Modulus); else Arg := Two_Pi * Argument / Cycle; return (Modulus * R (Cos (Double (Arg))), Modulus * R (Sin (Double (Arg)))); end if; else raise Argument_Error; end if; end Compose_From_Polar; --------------- -- Conjugate -- --------------- function Conjugate (X : Complex) return Complex is begin return Complex'(X.Re, -X.Im); end Conjugate; -------- -- Im -- -------- function Im (X : Complex) return Real'Base is begin return X.Im; end Im; function Im (X : Imaginary) return Real'Base is begin return R (X); end Im; ------------- -- Modulus -- ------------- function Modulus (X : Complex) return Real'Base is Re2, Im2 : R; begin begin Re2 := X.Re ** 2; -- To compute (a**2 + b**2) ** (0.5) when a**2 may be out of bounds, -- compute a * (1 + (b/a) **2) ** (0.5). On a machine where the -- squaring does not raise constraint_error but generates infinity, -- we can use an explicit comparison to determine whether to use -- the scaling expression. -- The scaling expression is computed in double format throughout -- in order to prevent inaccuracies on machines where not all -- immediate expressions are rounded, such as PowerPC. if Re2 > R'Last then raise Constraint_Error; end if; exception when Constraint_Error => return R (Double (abs (X.Re)) * Sqrt (1.0 + (Double (X.Im) / Double (X.Re)) ** 2)); end; begin Im2 := X.Im ** 2; if Im2 > R'Last then raise Constraint_Error; end if; exception when Constraint_Error => return R (Double (abs (X.Im)) * Sqrt (1.0 + (Double (X.Re) / Double (X.Im)) ** 2)); end; -- Now deal with cases of underflow. If only one of the squares -- underflows, return the modulus of the other component. If both -- squares underflow, use scaling as above. if Re2 = 0.0 then if X.Re = 0.0 then return abs (X.Im); elsif Im2 = 0.0 then if X.Im = 0.0 then return abs (X.Re); else if abs (X.Re) > abs (X.Im) then return R (Double (abs (X.Re)) * Sqrt (1.0 + (Double (X.Im) / Double (X.Re)) ** 2)); else return R (Double (abs (X.Im)) * Sqrt (1.0 + (Double (X.Re) / Double (X.Im)) ** 2)); end if; end if; else return abs (X.Im); end if; elsif Im2 = 0.0 then return abs (X.Re); -- In all other cases, the naive computation will do else return R (Sqrt (Double (Re2 + Im2))); end if; end Modulus; -------- -- Re -- -------- function Re (X : Complex) return Real'Base is begin return X.Re; end Re; ------------ -- Set_Im -- ------------ procedure Set_Im (X : in out Complex; Im : Real'Base) is begin X.Im := Im; end Set_Im; procedure Set_Im (X : out Imaginary; Im : Real'Base) is begin X := Imaginary (Im); end Set_Im; ------------ -- Set_Re -- ------------ procedure Set_Re (X : in out Complex; Re : Real'Base) is begin X.Re := Re; end Set_Re; end Ada.Numerics.Generic_Complex_Types;