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Length: 10240 (0x2800)
Types: Ada Source
Notes: 03_class, FILE, R1k_Segment, e3_tag, function Kf_Atanh, seg_0130ca, separate Generic_Elementary_Functions
└─⟦8527c1e9b⟧ Bits:30000544 8mm tape, Rational 1000, Arrival backup of disks in PAM's R1000
└─⟦5a81ac88f⟧ »Space Info Vol 1«
└─⟦this⟧
separate (Generic_Elementary_Functions)
function Kf_Atanh (Y : Common_Float) return Common_Float is
-- On input, |Y| <= 2(exp(1/16)-1) / (exp(1/16)+1).
-- On output, the value of [log(1 + Y/2) - log(1 - Y/2)]/Y - 1
-- is returned.
-- The core approximation calculates
-- Poly = [log(1 + Y/2) - log(1 - Y/2)]/Y - 1
-- in the type Working_Float, which is a type chosen to
-- have accuracy comparable to the base type of Float_Type.
Result : Common_Float;
begin
-- Approximation.
-- The following is the core approximation. We approximate
-- [log(1 + Y/2) - log(1 - Y/2)]/Y - 1
-- by a polynomial Poly. The case analysis finds both a suitable
-- floating-point type (less expensive to use than LONGEST_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 (Y * Y);
Poly := R * 8.33340_08285_51364E-02;
Result := 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 (Y * Y);
Poly := R * (8.33333_33333_33335_93622E-02 +
R * (1.24999_99997_81386_68903E-02 +
R * (2.23219_81075_85598_51206E-03)));
Result := 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 (Y * Y);
Poly := R * (8.33333_33333_33335_93622E-02 +
R * (1.24999_99997_81386_68903E-02 +
R * (2.23219_81075_85598_51206E-03)));
Result := 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 (Y * Y);
Poly := R * (8.33333_33333_33335_93622E-02 +
R * (1.24999_99997_81386_68903E-02 +
R * (2.23219_81075_85598_51206E-03)));
Result := 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 (Y * Y);
Poly :=
R *
(8.33333_33333_33333_33333_33334_07301_529E-02 +
R *
(1.24999_99999_99999_99998_61732_74718_869E-02 +
R *
(2.23214_28571_42866_13712_34336_23012_985E-03 +
R *
(4.34027_77751_26439_67391_35491_00214_979E-04 +
R *
(8.87820_39767_24501_02052_39367_49695_054E-05)))));
Result := 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 (Y * Y);
Poly :=
R *
(8.33333_33333_33333_33333_33333_33332_96298_39318E-02 +
R *
(1.25000_00000_00000_00000_00000_93488_19499_40702E-02 +
R *
(2.23214_28571_42857_14277_26598_59261_40273_30694E-03 +
R *
(4.34027_77777_77814_30973_20354_95180_362E-04 +
R *
(8.87784_09009_03777_78533_78449_15942_610E-05 +
R *
(1.87809_65740_24066_11924_19609_24471_232E-05))))));
Result := Common_Float (Poly);
end;
when others =>
raise Program_Error; -- assumption (1) is violated.
end case;
-- This completes the core approximation.
return (Result);
end Kf_Atanh;
nblk1=9
nid=0
hdr6=12
[0x00] rec0=1e rec1=00 rec2=01 rec3=030
[0x01] rec0=1f rec1=00 rec2=02 rec3=01a
[0x02] rec0=02 rec1=00 rec2=09 rec3=00c
[0x03] rec0=1b rec1=00 rec2=03 rec3=076
[0x04] rec0=00 rec1=00 rec2=08 rec3=00c
[0x05] rec0=1d rec1=00 rec2=04 rec3=000
[0x06] rec0=01 rec1=00 rec2=07 rec3=00c
[0x07] rec0=14 rec1=00 rec2=05 rec3=054
[0x08] rec0=10 rec1=00 rec2=06 rec3=000
tail 0x2150db54682b15180bf40 0x42a00066462061e03