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top - downloadIndex: ┃ B T ┃
Length: 6775 (0x1a77)
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_Atnsm (Y : Common_Float) return Common_Float is
-- On input, Y is a floating point value in Common_Float, |Y| <= 1/16;
-- On output, a Common_Float value is returned which represents the
-- approximation of atan(Y)-Y.
Q : Common_Float;
begin
-- The following is the core approximation. We approximate
-- exp(R1+R2)-1 by a 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 (Y);
S := R * R;
Poly := -R * S * (0.33333_23001 - S * (0.19918_59719));
Q := 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 (Y);
S := R * R;
Poly := -R * S *
(0.33333_33333_33331_70500 -
S * (0.19999_99999_93932_23405 -
S * (0.14285_71356_18071_69030 -
S * (0.11110_73628_35145_25407 -
S * (0.90029_81028_54497_84439E-01)))));
Q := 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 (Y);
S := R * R;
Poly := -R * S *
(0.33333_33333_33331_70500 -
S * (0.19999_99999_93932_23405 -
S * (0.14285_71356_18071_69030 -
S * (0.11110_73628_35145_25407 -
S * (0.90029_81028_54497_84439E-01)))));
Q := 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 (Y);
S := R * R;
Poly :=
-R * S *
(0.33333_33333_33333_33130_94892 -
S *
(0.19999_99999_99989_99552_86683 -
S *
(0.14285_71428_40674_81920_91353 -
S *
(0.11111_10986_45979_04500_50686 -
S *
(0.90904_31858_09744_75086_35684E-01 -
S * (0.76023_22269_40038_42302_02382E-01))))));
Q := 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 (Y);
S := R * R;
Poly :=
-R * S *
(0.33333_33333_33333_33333_33333_30640_688 -
S *
(0.19999_99999_99999_99999_99725_07169_093 -
S *
(0.14285_71428_57142_85704_61906_79692_957 -
S *
(0.11111_11111_11110_94447_44685_62289_640 -
S *
(0.90909_09090_89284_08030_74591_43510_263E-01 -
S *
(0.76923_07682_73618_54039_14363_83712_288E-01 -
S *
(0.66666_63192_87231_75829_95036_25183_458E-01 -
S *
(0.58815_92881_06830_95028_64129_28595_505E-01 -
S *
(0.51711_22330_76482_53731_52208_70654_932E-01)))))))));
Q := 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 (Y);
S := R * R;
Poly :=
-R * S *
(0.33333_33333_33333_33333_33333_33333_3304 -
S *
(0.19999_99999_99999_99999_99999_99956_0187 -
S *
(0.14285_71428_57142_85714_28569_15903_2129 -
S *
(0.11111_11111_11111_11111_05278_66512_9097 -
S *
(0.90909_09090_90909_08220_63173_05946_2434E-01 -
S *
(0.76923_07692_30761_06801_67642_90322_8423E-01 -
S *
(0.66666_66666_61651_60744_77042_68877_1500E-01 -
S *
(0.58823_52920_68496_03403_53270_56134_3084E-01 -
S *
(0.52631_52374_60356_91863_62352_54421_7989E-01 -
S *
(0.47609_62465_86213_53088_72992_19065_8779E-01 -
S *
(0.42553_42964_37218_11922_99573_45059_6737E-01)))))))))));
Q := Common_Float (Poly);
end;
when others =>
raise Program_Error; -- assumption (1) is violated.
end case;
-- This completes the core approximation.
return (Q);
end Kf_Atnsm;