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Length: 8145 (0x1fd1)
Types: TextFile
Names: »B«
└─⟦5f3412b64⟧ Bits:30000745 8mm tape, Rational 1000, ENVIRONMENT 12_6_5 TOOLS
└─⟦91c658230⟧ »DATA«
└─⟦458657fb6⟧
└─⟦1472c4407⟧
└─⟦this⟧
└─⟦d10a02448⟧ Bits:30000409 8mm tape, Rational 1000, ENVIRONMENT, D_12_7_3
└─⟦fc9b38f02⟧ »DATA«
└─⟦9b46a407a⟧
└─⟦2e03b931c⟧
└─⟦this⟧
separate (Generic_Elementary_Functions)
function Kf_Cos (Y1, Y2 : Common_Float) return Common_Float is
-- On input, Y1 and Y2 are floating point values in Common_Float;
-- These two variables represent the remainder of the reduced argument
-- X = N * (pi/2) + remainder, where |remainder| <= pi/4.
-- On output, a Common_Float value is returned which represents the
-- approximation of cos( Y1+Y2 ).
R1, R2, Rsq, Q : Common_Float;
begin
R1 := Y1;
R2 := Y2;
Rsq := R1 + R2;
Rsq := Rsq * Rsq;
-- The following is the core approximation. We approximate
-- cos(Y1+Y2) by an even polynomial. The case analysis finds both
-- a suitable floating-point type (less expensive to use than
-- Common_Float) and an appropriate polynomial approximation
-- that will deliver a result accurate enough with respect to
-- Float_Type'Base'Digits. Note that the upper bounds of the
-- cases below (6, 15, 16, 18, 27, and 33) are attributes
-- of predefined floating types of common systems.
case Float_Type'Base'Digits is
when 1 .. 6 =>
declare
type Working_Float is digits 6;
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly := 0.5 - S * (0.41666_65673E-01 -
S * (0.13887_77331E-02 -
S * (0.24478_79547E-04)));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when 7 .. 15 =>
declare
type Working_Float is
digits (15 + System.Max_Digits - abs (15 - System.Max_Digits)) /
2;
-- this is min( 15, System.Max_Digits )
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
0.5 -
S *
(0.41666_66666_66666_01903E-01 -
S *
(0.13888_88888_88744_48186E-02 -
S *
(0.24801_58728_96438_74032E-04 -
S *
(0.27557_31439_04201_86748E-06 -
S * (0.20875_72754_71895_52619E-08 -
S * (0.11359_83163_10688_30184E-10))))));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when 16 =>
declare
type Working_Float is
digits (16 + System.Max_Digits - abs (16 - System.Max_Digits)) /
2;
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
0.5 -
S *
(0.41666_66666_66666_01903E-01 -
S *
(0.13888_88888_88744_48186E-02 -
S *
(0.24801_58728_96438_74032E-04 -
S *
(0.27557_31439_04201_86748E-06 -
S * (0.20875_72754_71895_52619E-08 -
S * (0.11359_83163_10688_30184E-10))))));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when 17 .. 18 =>
declare
type Working_Float is
digits (18 + System.Max_Digits - abs (18 - System.Max_Digits)) /
2;
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
0.5 -
S *
(0.41666_66666_66666_66603_42153E-01 -
S *
(0.13888_88888_88888_71536_63177E-02 -
S *
(0.24801_58730_15691_85047_02943E-04 -
S *
(0.27557_31921_43827_45008_49677E-06 -
S *
(0.20876_75414_25307_03561_14757E-08 -
S *
(0.11470_26790_89435_73177_12619E-10 -
S *
(0.47369_66690_47318_75384_42068E-13)))))));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when 19 .. 27 =>
declare
type Working_Float is
digits (27 + System.Max_Digits - abs (27 - System.Max_Digits)) /
2;
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
0.5 -
S *
(0.41666_66666_66666_66666_66665_16383_4051E-01 -
S *
(0.13888_88888_88888_88888_88245_47342_9026E-02 -
S *
(0.24801_58730_15873_01576_57181_53770_2548E-04 -
S *
(0.27557_31922_39858_81219_61255_06316_8107E-06 -
S *
(0.20876_75698_78631_80489_36726_20113_1863E-08 -
S *
(0.11470_74559_61289_73694_98585_54814_7595E-10 -
S *
(0.47794_77003_63678_43164_38976_00318_0721E-13 -
S *
(0.15618_79265_92016_38912_62591_16219_0901E-15 -
S *
(0.40810_43877_26966_16816_80251_59059_3738E-18)))))))));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when 28 .. 33 =>
declare
type Working_Float is
digits (33 + System.Max_Digits - abs (33 - System.Max_Digits)) /
2;
R, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
0.5 -
S *
(0.41666_66666_66666_66666_66666_66666_6480E-01 -
S *
(0.13888_88888_88888_88888_88888_88877_6335E-02 -
S *
(0.24801_58730_15873_01587_30158_46180_0299E-04 -
S *
(0.27557_31922_39858_90652_55387_96436_4088E-06 -
S *
(0.20876_75698_78680_98976_51897_22915_8020E-08 -
S *
(0.11470_74559_77297_23343_14028_68248_0321E-10 -
S *
(0.47794_77332_38691_60941_21737_53668_2651E-13 -
S *
(0.15619_20696_74971_44814_63427_34672_9062E-15 -
S *
(0.41103_17454_13508_37011_88930_50799_6253E-18 -
S *
(0.88966_22926_27803_79129_98598_30659_9363E-21 -
S *
(0.16020_11193_30748_03892_30511_97354_2056E-23)))))))))));
Q := 1.0 - Rsq * Common_Float (Poly);
end;
when others =>
raise Program_Error; -- assumption (1) is violated.
end case;
-- This completes the core approximation.
return (Q);
end Kf_Cos;