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Diffstat (limited to 'gcc/ada/libgnat/a-numaux__darwin.adb')
| -rw-r--r-- | gcc/ada/libgnat/a-numaux__darwin.adb | 211 |
1 files changed, 0 insertions, 211 deletions
diff --git a/gcc/ada/libgnat/a-numaux__darwin.adb b/gcc/ada/libgnat/a-numaux__darwin.adb deleted file mode 100644 index 85fdd24..0000000 --- a/gcc/ada/libgnat/a-numaux__darwin.adb +++ /dev/null @@ -1,211 +0,0 @@ ------------------------------------------------------------------------------- --- -- --- GNAT RUN-TIME COMPONENTS -- --- -- --- A D A . N U M E R I C S . A U X -- --- -- --- B o d y -- --- (Apple OS X Version) -- --- -- --- Copyright (C) 1998-2020, 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. -- --- -- ------------------------------------------------------------------------------- - -package body Ada.Numerics.Aux is - - ----------------------- - -- Local subprograms -- - ----------------------- - - function Is_Nan (X : Double) return Boolean; - -- Return True iff X is a IEEE NaN value - - 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. - - -- The following two functions implement Chebishev approximations - -- of the trigonometric functions in their reduced domain. - -- These approximations have been computed using Maple. - - function Sine_Approx (X : Double) return Double; - function Cosine_Approx (X : Double) return Double; - - pragma Inline (Reduce); - pragma Inline (Sine_Approx); - pragma Inline (Cosine_Approx); - - ------------------- - -- Cosine_Approx -- - ------------------- - - function Cosine_Approx (X : Double) return Double is - XX : constant Double := X * X; - begin - return (((((16#8.DC57FBD05F640#E-08 * XX - - 16#4.9F7D00BF25D80#E-06) * XX - + 16#1.A019F7FDEFCC2#E-04) * XX - - 16#5.B05B058F18B20#E-03) * XX - + 16#A.AAAAAAAA73FA8#E-02) * XX - - 16#7.FFFFFFFFFFDE4#E-01) * XX - - 16#3.655E64869ECCE#E-14 + 1.0; - end Cosine_Approx; - - ----------------- - -- Sine_Approx -- - ----------------- - - function Sine_Approx (X : Double) return Double is - XX : constant Double := X * X; - begin - return (((((16#A.EA2D4ABE41808#E-09 * XX - - 16#6.B974C10F9D078#E-07) * XX - + 16#2.E3BC673425B0E#E-05) * XX - - 16#D.00D00CCA7AF00#E-04) * XX - + 16#2.222222221B190#E-02) * XX - - 16#2.AAAAAAAAAAA44#E-01) * (XX * X) + X; - end Sine_Approx; - - ------------ - -- 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; - - ------------ - -- 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; - - --------- - -- Cos -- - --------- - - function Cos (X : Double) return Double is - Reduced_X : Double := abs X; - Quadrant : Natural range 0 .. 3; - - begin - if Reduced_X > Pi / 4.0 then - Reduce (Reduced_X, Quadrant); - - case Quadrant is - when 0 => - return Cosine_Approx (Reduced_X); - - when 1 => - return Sine_Approx (-Reduced_X); - - when 2 => - return -Cosine_Approx (Reduced_X); - - when 3 => - return Sine_Approx (Reduced_X); - end case; - end if; - - return Cosine_Approx (Reduced_X); - end Cos; - - --------- - -- Sin -- - --------- - - function Sin (X : Double) return Double is - Reduced_X : Double := X; - Quadrant : Natural range 0 .. 3; - - begin - if abs X > Pi / 4.0 then - Reduce (Reduced_X, Quadrant); - - case Quadrant is - when 0 => - return Sine_Approx (Reduced_X); - - when 1 => - return Cosine_Approx (Reduced_X); - - when 2 => - return Sine_Approx (-Reduced_X); - - when 3 => - return -Cosine_Approx (Reduced_X); - end case; - end if; - - return Sine_Approx (Reduced_X); - end Sin; - -end Ada.Numerics.Aux; |