--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/gcc/ada/libgnat/a-numaux__x86.adb	Fri Oct 27 22:46:09 2017 +0900
@@ -0,0 +1,577 @@
+------------------------------------------------------------------------------
+--                                                                          --
+--                         GNAT RUN-TIME COMPONENTS                         --
+--                                                                          --
+--                     A D A . N U M E R I C S . A U X                      --
+--                                                                          --
+--                                 B o d y                                  --
+--                        (Machine Version for x86)                         --
+--                                                                          --
+--          Copyright (C) 1998-2017, 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 System.Machine_Code; use System.Machine_Code;
+
+package body Ada.Numerics.Aux is
+
+   NL : constant String := ASCII.LF & ASCII.HT;
+
+   -----------------------
+   -- Local subprograms --
+   -----------------------
+
+   function Is_Nan (X : Double) return Boolean;
+   --  Return True iff X is a IEEE NaN value
+
+   function Logarithmic_Pow (X, Y : Double) return Double;
+   --  Implementation of X**Y using Exp and Log functions (binary base)
+   --  to calculate the exponentiation. This is used by Pow for values
+   --  for values of Y in the open interval (-0.25, 0.25)
+
+   procedure Reduce (X : in out Double; Q : out Natural);
+   --  Implement reduction of X by Pi/2. Q is the quadrant of the final
+   --  result in the range 0..3. The absolute value of X is at most Pi/4.
+   --  It is needed to avoid a loss of accuracy for sin near Pi and cos
+   --  near Pi/2 due to the use of an insufficiently precise value of Pi
+   --  in the range reduction.
+
+   pragma Inline (Is_Nan);
+   pragma Inline (Reduce);
+
+   --------------------------------
+   -- Basic Elementary Functions --
+   --------------------------------
+
+   --  This section implements a few elementary functions that are used to
+   --  build the more complex ones. This ordering enables better inlining.
+
+   ----------
+   -- Atan --
+   ----------
+
+   function Atan (X : Double) return Double is
+      Result  : Double;
+
+   begin
+      Asm (Template =>
+           "fld1" & NL
+         & "fpatan",
+         Outputs  => Double'Asm_Output ("=t", Result),
+         Inputs   => Double'Asm_Input  ("0", X));
+
+      --  The result value is NaN iff input was invalid
+
+      if not (Result = Result) then
+         raise Argument_Error;
+      end if;
+
+      return Result;
+   end Atan;
+
+   ---------
+   -- Exp --
+   ---------
+
+   function Exp (X : Double) return Double is
+      Result : Double;
+   begin
+      Asm (Template =>
+         "fldl2e               " & NL
+       & "fmulp   %%st, %%st(1)" & NL -- X * log2 (E)
+       & "fld     %%st(0)      " & NL
+       & "frndint              " & NL -- Integer (X * Log2 (E))
+       & "fsubr   %%st, %%st(1)" & NL -- Fraction (X * Log2 (E))
+       & "fxch                 " & NL
+       & "f2xm1                " & NL -- 2**(...) - 1
+       & "fld1                 " & NL
+       & "faddp   %%st, %%st(1)" & NL -- 2**(Fraction (X * Log2 (E)))
+       & "fscale               " & NL -- E ** X
+       & "fstp    %%st(1)      ",
+         Outputs  => Double'Asm_Output ("=t", Result),
+         Inputs   => Double'Asm_Input  ("0", X));
+      return Result;
+   end Exp;
+
+   ------------
+   -- Is_Nan --
+   ------------
+
+   function Is_Nan (X : Double) return Boolean is
+   begin
+      --  The IEEE NaN values are the only ones that do not equal themselves
+
+      return X /= X;
+   end Is_Nan;
+
+   ---------
+   -- Log --
+   ---------
+
+   function Log (X : Double) return Double is
+      Result : Double;
+
+   begin
+      Asm (Template =>
+         "fldln2               " & NL
+       & "fxch                 " & NL
+       & "fyl2x                " & NL,
+         Outputs  => Double'Asm_Output ("=t", Result),
+         Inputs   => Double'Asm_Input  ("0", X));
+      return Result;
+   end Log;
+
+   ------------
+   -- Reduce --
+   ------------
+
+   procedure Reduce (X : in out Double; Q : out Natural) is
+      Half_Pi     : constant := Pi / 2.0;
+      Two_Over_Pi : constant := 2.0 / Pi;
+
+      HM : constant := Integer'Min (Double'Machine_Mantissa / 2, Natural'Size);
+      M  : constant Double := 0.5 + 2.0**(1 - HM); -- Splitting constant
+      P1 : constant Double := Double'Leading_Part (Half_Pi, HM);
+      P2 : constant Double := Double'Leading_Part (Half_Pi - P1, HM);
+      P3 : constant Double := Double'Leading_Part (Half_Pi - P1 - P2, HM);
+      P4 : constant Double := Double'Leading_Part (Half_Pi - P1 - P2 - P3, HM);
+      P5 : constant Double := Double'Leading_Part (Half_Pi - P1 - P2 - P3
+                                                                 - P4, HM);
+      P6 : constant Double := Double'Model (Half_Pi - P1 - P2 - P3 - P4 - P5);
+      K  : Double;
+      R  : Integer;
+
+   begin
+      --  For X < 2.0**HM, all products below are computed exactly.
+      --  Due to cancellation effects all subtractions are exact as well.
+      --  As no double extended floating-point number has more than 75
+      --  zeros after the binary point, the result will be the correctly
+      --  rounded result of X - K * (Pi / 2.0).
+
+      K := X * Two_Over_Pi;
+      while abs K >= 2.0**HM loop
+         K := K * M - (K * M - K);
+         X :=
+           (((((X - K * P1) - K * P2) - K * P3) - K * P4) - K * P5) - K * P6;
+         K := X * Two_Over_Pi;
+      end loop;
+
+      --  If K is not a number (because X was not finite) raise exception
+
+      if Is_Nan (K) then
+         raise Constraint_Error;
+      end if;
+
+      --  Go through an integer temporary so as to use machine instructions
+
+      R := Integer (Double'Rounding (K));
+      Q := R mod 4;
+      K := Double (R);
+      X := (((((X - K * P1) - K * P2) - K * P3) - K * P4) - K * P5) - K * P6;
+   end Reduce;
+
+   ----------
+   -- Sqrt --
+   ----------
+
+   function Sqrt (X : Double) return Double is
+      Result  : Double;
+
+   begin
+      if X < 0.0 then
+         raise Argument_Error;
+      end if;
+
+      Asm (Template => "fsqrt",
+           Outputs  => Double'Asm_Output ("=t", Result),
+           Inputs   => Double'Asm_Input  ("0", X));
+
+      return Result;
+   end Sqrt;
+
+   --------------------------------
+   -- Other Elementary Functions --
+   --------------------------------
+
+   --  These are built using the previously implemented basic functions
+
+   ----------
+   -- Acos --
+   ----------
+
+   function Acos (X : Double) return Double is
+      Result  : Double;
+
+   begin
+      Result := 2.0 * Atan (Sqrt ((1.0 - X) / (1.0 + X)));
+
+      --  The result value is NaN iff input was invalid
+
+      if Is_Nan (Result) then
+         raise Argument_Error;
+      end if;
+
+      return Result;
+   end Acos;
+
+   ----------
+   -- Asin --
+   ----------
+
+   function Asin (X : Double) return Double is
+      Result  : Double;
+
+   begin
+      Result := Atan (X / Sqrt ((1.0 - X) * (1.0 + X)));
+
+      --  The result value is NaN iff input was invalid
+
+      if Is_Nan (Result) then
+         raise Argument_Error;
+      end if;
+
+      return Result;
+   end Asin;
+
+   ---------
+   -- Cos --
+   ---------
+
+   function Cos (X : Double) return Double is
+      Reduced_X : Double := abs X;
+      Result    : Double;
+      Quadrant  : Natural range 0 .. 3;
+
+   begin
+      if Reduced_X > Pi / 4.0 then
+         Reduce (Reduced_X, Quadrant);
+
+         case Quadrant is
+            when 0 =>
+               Asm (Template  => "fcos",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+
+            when 1 =>
+               Asm (Template  => "fsin",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", -Reduced_X));
+
+            when 2 =>
+               Asm (Template  => "fcos ; fchs",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+
+            when 3 =>
+               Asm (Template  => "fsin",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+         end case;
+
+      else
+         Asm (Template  => "fcos",
+              Outputs  => Double'Asm_Output ("=t", Result),
+              Inputs   => Double'Asm_Input  ("0", Reduced_X));
+      end if;
+
+      return Result;
+   end Cos;
+
+   ---------------------
+   -- Logarithmic_Pow --
+   ---------------------
+
+   function Logarithmic_Pow (X, Y : Double) return Double is
+      Result  : Double;
+   begin
+      Asm (Template => ""             --  X                  : Y
+       & "fyl2x                " & NL --  Y * Log2 (X)
+       & "fld     %%st(0)      " & NL --  Y * Log2 (X)       : Y * Log2 (X)
+       & "frndint              " & NL --  Int (...)          : Y * Log2 (X)
+       & "fsubr   %%st, %%st(1)" & NL --  Int (...)          : Fract (...)
+       & "fxch                 " & NL --  Fract (...)        : Int (...)
+       & "f2xm1                " & NL --  2**Fract (...) - 1 : Int (...)
+       & "fld1                 " & NL --  1 : 2**Fract (...) - 1 : Int (...)
+       & "faddp   %%st, %%st(1)" & NL --  2**Fract (...)     : Int (...)
+       & "fscale               ",     --  2**(Fract (...) + Int (...))
+         Outputs  => Double'Asm_Output ("=t", Result),
+         Inputs   =>
+           (Double'Asm_Input  ("0", X),
+            Double'Asm_Input  ("u", Y)));
+      return Result;
+   end Logarithmic_Pow;
+
+   ---------
+   -- Pow --
+   ---------
+
+   function Pow (X, Y : Double) return Double is
+      type Mantissa_Type is mod 2**Double'Machine_Mantissa;
+      --  Modular type that can hold all bits of the mantissa of Double
+
+      --  For negative exponents, do divide at the end of the processing
+
+      Negative_Y : constant Boolean := Y < 0.0;
+      Abs_Y      : constant Double := abs Y;
+
+      --  During this function the following invariant is kept:
+      --  X ** (abs Y) = Base**(Exp_High + Exp_Mid + Exp_Low) * Factor
+
+      Base : Double := X;
+
+      Exp_High : Double := Double'Floor (Abs_Y);
+      Exp_Mid  : Double;
+      Exp_Low  : Double;
+      Exp_Int  : Mantissa_Type;
+
+      Factor : Double := 1.0;
+
+   begin
+      --  Select algorithm for calculating Pow (integer cases fall through)
+
+      if Exp_High >= 2.0**Double'Machine_Mantissa then
+
+         --  In case of Y that is IEEE infinity, just raise constraint error
+
+         if Exp_High > Double'Safe_Last then
+            raise Constraint_Error;
+         end if;
+
+         --  Large values of Y are even integers and will stay integer
+         --  after division by two.
+
+         loop
+            --  Exp_Mid and Exp_Low are zero, so
+            --    X**(abs Y) = Base ** Exp_High = (Base**2) ** (Exp_High / 2)
+
+            Exp_High := Exp_High / 2.0;
+            Base := Base * Base;
+            exit when Exp_High < 2.0**Double'Machine_Mantissa;
+         end loop;
+
+      elsif Exp_High /= Abs_Y then
+         Exp_Low := Abs_Y - Exp_High;
+         Factor := 1.0;
+
+         if Exp_Low /= 0.0 then
+
+            --  Exp_Low now is in interval (0.0, 1.0)
+            --  Exp_Mid := Double'Floor (Exp_Low * 4.0) / 4.0;
+
+            Exp_Mid := 0.0;
+            Exp_Low := Exp_Low - Exp_Mid;
+
+            if Exp_Low >= 0.5 then
+               Factor := Sqrt (X);
+               Exp_Low := Exp_Low - 0.5;  -- exact
+
+               if Exp_Low >= 0.25 then
+                  Factor := Factor * Sqrt (Factor);
+                  Exp_Low := Exp_Low - 0.25; --  exact
+               end if;
+
+            elsif Exp_Low >= 0.25 then
+               Factor := Sqrt (Sqrt (X));
+               Exp_Low := Exp_Low - 0.25; --  exact
+            end if;
+
+            --  Exp_Low now is in interval (0.0, 0.25)
+
+            --  This means it is safe to call Logarithmic_Pow
+            --  for the remaining part.
+
+            Factor := Factor * Logarithmic_Pow (X, Exp_Low);
+         end if;
+
+      elsif X = 0.0 then
+         return 0.0;
+      end if;
+
+      --  Exp_High is non-zero integer smaller than 2**Double'Machine_Mantissa
+
+      Exp_Int := Mantissa_Type (Exp_High);
+
+      --  Standard way for processing integer powers > 0
+
+      while Exp_Int > 1 loop
+         if (Exp_Int and 1) = 1 then
+
+            --  Base**Y = Base**(Exp_Int - 1) * Exp_Int for Exp_Int > 0
+
+            Factor := Factor * Base;
+         end if;
+
+         --  Exp_Int is even and Exp_Int > 0, so
+         --    Base**Y = (Base**2)**(Exp_Int / 2)
+
+         Base := Base * Base;
+         Exp_Int := Exp_Int / 2;
+      end loop;
+
+      --  Exp_Int = 1 or Exp_Int = 0
+
+      if Exp_Int = 1 then
+         Factor := Base * Factor;
+      end if;
+
+      if Negative_Y then
+         Factor := 1.0 / Factor;
+      end if;
+
+      return Factor;
+   end Pow;
+
+   ---------
+   -- Sin --
+   ---------
+
+   function Sin (X : Double) return Double is
+      Reduced_X : Double := X;
+      Result    : Double;
+      Quadrant  : Natural range 0 .. 3;
+
+   begin
+      if abs X > Pi / 4.0 then
+         Reduce (Reduced_X, Quadrant);
+
+         case Quadrant is
+            when 0 =>
+               Asm (Template  => "fsin",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+
+            when 1 =>
+               Asm (Template  => "fcos",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+
+            when 2 =>
+               Asm (Template  => "fsin",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", -Reduced_X));
+
+            when 3 =>
+               Asm (Template  => "fcos ; fchs",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+         end case;
+
+      else
+         Asm (Template  => "fsin",
+            Outputs  => Double'Asm_Output ("=t", Result),
+            Inputs   => Double'Asm_Input  ("0", Reduced_X));
+      end if;
+
+      return Result;
+   end Sin;
+
+   ---------
+   -- Tan --
+   ---------
+
+   function Tan (X : Double) return Double is
+      Reduced_X : Double := X;
+      Result    : Double;
+      Quadrant  : Natural range 0 .. 3;
+
+   begin
+      if abs X > Pi / 4.0 then
+         Reduce (Reduced_X, Quadrant);
+
+         if Quadrant mod 2 = 0 then
+            Asm (Template  => "fptan" & NL
+                            & "ffree   %%st(0)"  & NL
+                            & "fincstp",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+         else
+            Asm (Template  => "fsincos" & NL
+                            & "fdivp   %%st, %%st(1)" & NL
+                            & "fchs",
+                  Outputs  => Double'Asm_Output ("=t", Result),
+                  Inputs   => Double'Asm_Input  ("0", Reduced_X));
+         end if;
+
+      else
+         Asm (Template  =>
+               "fptan                 " & NL
+             & "ffree   %%st(0)      " & NL
+             & "fincstp              ",
+               Outputs  => Double'Asm_Output ("=t", Result),
+               Inputs   => Double'Asm_Input  ("0", Reduced_X));
+      end if;
+
+      return Result;
+   end Tan;
+
+   ----------
+   -- Sinh --
+   ----------
+
+   function Sinh (X : Double) return Double is
+   begin
+      --  Mathematically Sinh (x) is defined to be (Exp (X) - Exp (-X)) / 2.0
+
+      if abs X < 25.0 then
+         return (Exp (X) - Exp (-X)) / 2.0;
+      else
+         return Exp (X) / 2.0;
+      end if;
+   end Sinh;
+
+   ----------
+   -- Cosh --
+   ----------
+
+   function Cosh (X : Double) return Double is
+   begin
+      --  Mathematically Cosh (X) is defined to be (Exp (X) + Exp (-X)) / 2.0
+
+      if abs X < 22.0 then
+         return (Exp (X) + Exp (-X)) / 2.0;
+      else
+         return Exp (X) / 2.0;
+      end if;
+   end Cosh;
+
+   ----------
+   -- Tanh --
+   ----------
+
+   function Tanh (X : Double) return Double is
+   begin
+      --  Return the Hyperbolic Tangent of x
+
+      --                                    x    -x
+      --                                   e  - e        Sinh (X)
+      --       Tanh (X) is defined to be -----------   = --------
+      --                                    x    -x      Cosh (X)
+      --                                   e  + e
+
+      if abs X > 23.0 then
+         return Double'Copy_Sign (1.0, X);
+      end if;
+
+      return 1.0 / (1.0 + Exp (-(2.0 * X))) - 1.0 / (1.0 + Exp (2.0 * X));
+   end Tanh;
+
+end Ada.Numerics.Aux;