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Length: 6726 (0x1a46)
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_Em1sm (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 * log2/32 + remainder, where |remainder| <= log2/64.
-- On output, a Common_Float value is returned which represents the
-- approximation of exp(Y1+Y2)-1 for small numbers.
R1, R2, Q : Common_Float;
begin
R1 := Y1;
R2 := Y2;
-- 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, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly := R * R * (5.00004_0481E-01 + R * 1.66667_6443E-01);
Q := R1 + (R2 + 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, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly := R * R *
(5.00000_00000_00000_08883E-01 +
R * (1.66666_66666_52608_78863E-01 +
R * (4.16666_66666_22607_95726E-02 +
R * (8.33336_79843_42196_16221E-03 +
R * (1.38889_49086_37771_99667E-03)))));
Q := R1 + (R2 + Common_Float (Poly));
end;
when 16 =>
declare
type Working_Float is
digits (16 + System.Max_Digits - abs (16 - System.Max_Digits)) /
2;
R, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly := R * R *
(5.00000_00000_00000_08883E-01 +
R * (1.66666_66666_52608_78863E-01 +
R * (4.16666_66666_22607_95726E-02 +
R * (8.33336_79843_42196_16221E-03 +
R * (1.38889_49086_37771_99667E-03)))));
Q := R1 + (R2 + Common_Float (Poly));
end;
when 17 .. 18 =>
declare
type Working_Float is
digits (18 + System.Max_Digits - abs (18 - System.Max_Digits)) /
2;
R, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly :=
R * R *
(5.00000_00000_00000_07339E-01 +
R * (1.66666_66666_66666_69177E-01 +
R * (4.16666_66666_28680_32559E-02 +
R * (8.33333_33332_52083_91118E-03 +
R * (1.38889_44766_51246_30293E-03 +
R * (1.98413_53190_32208_33704E-04))))));
Q := R1 + (R2 + Common_Float (Poly));
end;
when 19 .. 27 =>
declare
type Working_Float is
digits (27 + System.Max_Digits - abs (27 - System.Max_Digits)) /
2;
R, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly :=
R * R *
(4.99999_99999_99999_99999_99636_21075E-01 +
R *
(1.66666_66666_66666_66666_66512_04136E-01 +
R *
(4.16666_66666_66666_69681_59325_03184E-02 +
R *
(8.33333_33333_33333_40906_33326_46233E-03 +
R *
(1.38888_88888_81124_92492_26093_01620E-03 +
R *
(1.98412_69841_13983_54303_59568_15543E-04 +
R *
(2.48016_66086_20855_39725_92760_56125E-05 +
R *
(2.75574_13983_51388_82843_29291_74995E-06))))))));
Q := R1 + (R2 + Common_Float (Poly));
end;
when 28 .. 33 =>
declare
type Working_Float is
digits (33 + System.Max_Digits - abs (33 - System.Max_Digits)) /
2;
R, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
Poly :=
R * R *
(5.0E-01 +
R *
(1.66666_66666_66666_66666_66666_66668_18891E-01 +
R *
(4.16666_66666_66666_66666_66666_66671_98062E-02 +
R *
(8.33333_33333_33333_33333_33182_72433_96473E-03 +
R *
(1.38888_88888_88888_88888_88860_77788_96115E-03 +
R *
(1.98412_69841_26984_13216_98830_39302_820E-04 +
R *
(2.48015_87301_58730_16549_32617_44006_810E-05 +
R *
(2.75573_19223_90497_50521_23337_44713_411E-06 +
R *
(2.75573_19223_90383_09381_24531_22474_208E-07 +
R *
(2.50521_67036_89710_14700_24557_88635_351E-08 +
R *
(2.08768_06002_87469_73970_46716_40247_597E-09)))))))))));
Q := R1 + (R2 + Common_Float (Poly));
end;
when others =>
raise Program_Error; -- assumption (1) is violated.
end case;
-- This completes the core approximation.
return (Q);
end Kf_Em1sm;