------------------------------------------------------------------------------
-- --
--- GNAT RUNTIME COMPONENTS --
+-- GNAT RUN-TIME COMPONENTS --
-- --
-- ADA.NUMERICS.GENERIC_COMPLEX_ELEMENTARY_FUNCTIONS --
-- --
-- B o d y --
-- --
--- $Revision: 1.13 $
--- --
--- Copyright (C) 1992-2001 Free Software Foundation, Inc.
+-- 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 2, or (at your option) any later ver- --
+-- 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. See the GNU General Public License --
--- for more details. You should have received a copy of the GNU General --
--- Public License distributed with GNAT; see file COPYING. If not, write --
--- to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, --
--- MA 02111-1307, USA. --
+-- 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. --
-- --
--- As a special exception, if other files instantiate generics from this --
--- unit, or you link this unit with other files to produce an executable, --
--- this unit does not by itself cause the resulting executable to be --
--- covered by the GNU General Public License. This exception does not --
--- however invalidate any other reasons why the executable file might be --
--- covered by the GNU Public License. --
+-- 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. --
--- It is now maintained by Ada Core Technologies Inc (http://www.gnat.com). --
+-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
end Arccot;
--------------
- -- Arctcoth --
+ -- Arccoth --
--------------
function Arccoth (X : Complex) return Complex is
Result : Complex;
begin
+ -- For very small argument, sin (x) = x
+
if abs Re (X) < Square_Root_Epsilon and then
abs Im (X) < Square_Root_Epsilon
then
elsif Im (Result) < -PI_2 then
Set_Im (Result, -(PI + Im (X)));
end if;
+
+ return Result;
end if;
Result := -Complex_I * Log (Complex_I * X + Sqrt (1.0 - X * X));
then
Result := Log_Two + Log (X); -- may have wrong sign
- if (Re (X) < 0.0 and Re (Result) > 0.0)
- or else (Re (X) > 0.0 and Re (Result) < 0.0)
+ if (Re (X) < 0.0 and then Re (Result) > 0.0)
+ or else (Re (X) > 0.0 and then Re (Result) < 0.0)
then
Set_Re (Result, -Re (Result));
end if;
return
Compose_From_Cartesian
(Cos (Re (X)) * Cosh (Im (X)),
- -Sin (Re (X)) * Sinh (Im (X)));
+ -(Sin (Re (X)) * Sinh (Im (X))));
end Cos;
----------
---------
function Exp (X : Complex) return Complex is
- EXP_RE_X : Real'Base := Exp (Re (X));
+ EXP_RE_X : constant Real'Base := Exp (Re (X));
begin
return Compose_From_Cartesian (EXP_RE_X * Cos (Im (X)),
EXP_RE_X * Sin (Im (X)));
end Exp;
-
function Exp (X : Imaginary) return Complex is
- ImX : Real'Base := Im (X);
+ ImX : constant Real'Base := Im (X);
begin
return Compose_From_Cartesian (Cos (ImX), Sin (ImX));
end if;
end if;
- if Im (X) < 0.0 then -- halve angle, Sqrt of magnitude
+ if Im (X) < 0.0 then -- halve angle, Sqrt of magnitude
R_Y := -R_Y;
end if;
return Compose_From_Cartesian (R_X, R_Y);
exception
when Constraint_Error =>
- -- Rescale and try again.
+ -- Rescale and try again
R := Modulus (Compose_From_Cartesian (Re (X / 4.0), Im (X / 4.0)));
R_X := 2.0 * Sqrt (0.5 * R + 0.5 * Re (X / 4.0));
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