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top - downloadIndex: ┃ B T ┃
Length: 8694 (0x21f6)
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_Sin (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 sin( Y1+Y2 ).
R1, R2, Q : Common_Float;
begin
R1 := Y1;
R2 := Y2;
-- The following is the core approximation. We approximate
-- sin(Y1+Y2) by an odd 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 := S * (0.16666_66269E-0 -
S * (0.83329_37955E-2 -
S * (0.19729_49430E-3 - S * (0.17898_67484E-5))));
Q := R1 + (R2 - (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, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
S *
(0.16666_66666_66666_62965E-00 -
S *
(0.83333_33333_33216_57487E-02 -
S *
(0.19841_26984_00425_50051E-03 -
S *
(0.27557_31863_01054_79460E-05 -
S *
(0.25051_96268_35442_39751E-07 -
S *
(0.16041_33183_44428_30041E-09 -
S *
(0.67810_12820_36054_53944E-12)))))));
Q := R1 + (R2 - (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, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
S *
(0.16666_66666_66666_62965E-00 -
S *
(0.83333_33333_33216_57487E-02 -
S *
(0.19841_26984_00425_50051E-03 -
S *
(0.27557_31863_01054_79460E-05 -
S *
(0.25051_96268_35442_39751E-07 -
S *
(0.16041_33183_44428_30041E-09 -
S *
(0.67810_12820_36054_53944E-12)))))));
Q := R1 + (R2 - (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, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
S *
(0.16666_66666_66666_66663_05265E-00 -
S *
(0.83333_33333_33333_18353_27331E-02 -
S *
(0.19841_26984_12677_42397_98061E-03 -
S *
(0.27557_31922_25915_00034_88464E-05 -
S *
(0.25052_10788_96438_73197_48920E-07 -
S *
(0.16058_94677_96247_63281_41150E-09 -
S *
(0.76372_69506_69707_85652_27420E-12 -
S *
(0.23950_00674_30593_53449_39104E-14))))))));
Q := R1 + (R2 - (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, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
S *
(0.16666_66666_66666_66666_66666_66633_0086E+00 -
S *
(0.83333_33333_33333_33333_33330_76943_0210E-02 -
S *
(0.19841_26984_12698_41269_83450_93722_6766E-03 -
S *
(0.27557_31922_39858_90643_73301_78259_2770E-05 -
S *
(0.25052_10838_54417_12158_37226_81690_8857E-07 -
S *
(0.16059_04383_68185_46636_41083_91388_2129E-09 -
S *
(0.76471_63730_91063_93957_96779_08149_5627E-12 -
S *
(0.28114_57081_79321_12323_34834_60010_1450E-14 -
S *
(0.82204_32293_08044_34287_39069_99726_9855E-17 -
S *
(0.19438_17832_99374_63087_47164_67848_4712E-19))))))))));
Q := R1 + (R2 - (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, S, Poly : Working_Float;
begin
R := Working_Float (R1 + R2);
S := R * R;
Poly :=
S *
(0.16666_66666_66666_66666_66666_66666_6666E+00 -
S *
(0.83333_33333_33333_33333_33333_33333_0274E-02 -
S *
(0.19841_26984_12698_41269_84126_98311_2600E-03 -
S *
(0.27557_31922_39858_90652_55730_24207_5442E-05 -
S *
(0.25052_10838_54417_18775_03589_32984_9329E-07 -
S *
(0.16059_04383_68216_14589_51327_14046_5961E-09 -
S *
(0.76471_63731_81981_25083_98331_27914_0063E-12 -
S *
(0.28114_57254_34445_07256_92700_63990_6368E-14 -
S *
(0.82206_35244_69072_20561_89193_97777_7182E-17 -
S *
(0.19572_93878_24940_42631_49760_79163_7901E-19 -
S *
(0.38680_05154_37551_58372_98445_80258_9098E-22 -
S *
(0.63830_99586_87078_27791_97302_21097_2554E-25))))))))))));
Q := R1 + (R2 - (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_Sin;