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Length: 7168 (0x1c00)
Types: Ada Source
Notes: 03_class, FILE, R1k_Segment, e3_tag, function Arctan, seg_0130c1, separate Generic_Elementary_Functions
└─⟦8527c1e9b⟧ Bits:30000544 8mm tape, Rational 1000, Arrival backup of disks in PAM's R1000
└─⟦cfc2e13cd⟧ »Space Info Vol 2«
└─⟦this⟧
separate (Generic_Elementary_Functions)
function Arctan (Y : Float_Type; X : Float_Type := 1.0) return Float_Type is
U, V, Sign_X, Sign_Y, Buffer, Z1, Z2, Result : Common_Float;
Swap_Flag : Boolean;
Zero : constant := 0.0;
One : constant := 1.0;
Pi : constant := 3.14159_26535_89793_23846_26433_83279_50288_4197;
Pi_By_2 : constant := 1.57079_63267_94896_61923_13216_91639_75144_2098;
Pi_By_4 : constant := 0.78539_81633_97448_30961_56608_45819_87572_1049;
Pi_3_4 : constant := 2.35619_44901_92344_92884_69825_37459_62716_3147;
Pi_Lead : constant Common_Float := 16#3.243#;
Piby2_Lead : constant Common_Float := 16#1.921#;
Pi_Trail : constant Common_Float :=
16#0.F6A88_85A30_8D313_198A2_E0370_7344A_40938#E-3;
Piby2_Trail : constant Common_Float :=
16#0.FB544_42D18_46989_8CC51_701B8_39A25_2049C#E-3;
begin
-- Filter out exceptional cases.
U := Common_Float (X);
Sign_X := Copy_Sign (One, U);
U := abs (U);
V := Common_Float (Y);
Sign_Y := Copy_Sign (One, V);
V := abs (V);
if V = Zero then
if U = Zero then
raise Argument_Error;
else
if Sign_X = One then
return (Float_Type (Copy_Sign (Zero, Sign_Y)));
else
return (Float_Type (Sign_Y * Pi));
end if;
end if;
end if;
if U = Zero then
return (Float_Type (Sign_Y * Pi_By_2));
end if;
if U = V then
if Sign_X = One then
return (Float_Type (Sign_Y * Pi_By_4));
else
return (Float_Type (Sign_Y * Pi_3_4));
end if;
end if;
-- Step 1. Argument Reduction.
if U < V then
Swap_Flag := True;
Buffer := U;
U := V;
V := Buffer;
else
Swap_Flag := False;
end if;
-- Step 2. Approximation. Obtain atan(V/U). This is performed by KP_Atn
-- which returns atan(V/U) as Z1 + Z2. Moreover, whenever Z1 is non-zero,
-- it has at most 4 hex digits and satisfies |Z1| >= 1/16.
Kp_Atn (V, U, Z1, Z2);
-- Step 3. Reconstruction. Obtain atan(Y,X) via Sign_X, Sign_Y, Swap_Flag,
-- and atan(V/U). The reconstruction is based on three relations:
-- atan(Y,X) = sign(Y) * atan(|Y|,X),
-- atan(|Y|,X) = pi - atan(|Y|,-X),
-- atan(|Y|,|X|) = pi/2 - atan(|X|,|Y|).
if Swap_Flag = False then
if Sign_X = One then
-- atan(|Y|,X) = atan(V,U)
Result := Z1 + Z2;
else
-- atan(|Y|,X) = atan(V,-U) = pi - atan(V,U)
Result := (Pi_Lead - Z1) + (Pi_Trail - Z2);
end if;
else
if Sign_X = One then
-- atan(|Y|,X) = atan(U,V) = pi/2 - atan(V,U)
Result := (Piby2_Lead - Z1) + (Piby2_Trail - Z2);
else
-- atan(|Y|,X) = atan(U,-V) = pi - atan(U,V) = pi - (pi/2 - atan(V,U))
Result := (Piby2_Lead + Z1) + (Piby2_Trail + Z2);
end if;
end if;
return (Float_Type (Copy_Sign (Result, Sign_Y)));
end Arctan;
nblk1=6
nid=0
hdr6=c
[0x00] rec0=1c rec1=00 rec2=01 rec3=020
[0x01] rec0=01 rec1=00 rec2=06 rec3=014
[0x02] rec0=2e rec1=00 rec2=02 rec3=02e
[0x03] rec0=00 rec1=00 rec2=05 rec3=03a
[0x04] rec0=20 rec1=00 rec2=03 rec3=00a
[0x05] rec0=06 rec1=00 rec2=04 rec3=000
tail 0x2170e741e82b15170df77 0x42a00066462061e03