1 |
2 | sacos.sa 3.3 12/19/90
3 |
4 | Description: The entry point sAcos com
5 | an input argument; sAcosd does
6 | input.
7 |
8 | Input: Double-extended number X in loc
9 | by address register a0.
10 |
11 | Output: The value arccos(X) returned i
12 |
13 | Accuracy and Monotonicity: The returne
14 | 64 significant bit, i.e. withi
15 | result is subsequently rounded
16 | result is provably monotonic i
17 |
18 | Speed: The program sCOS takes approxim
19 |
20 | Algorithm:
21 |
22 | ACOS
23 | 1. If |X| >= 1, go to 3.
24 |
25 | 2. (|X| < 1) Calculate acos(X) by
26 | z := (1-X) / (1+X)
27 | acos(X) = 2 * atan( sqrt(z) ).
28 | Exit.
29 |
30 | 3. If |X| > 1, go to 5.
31 |
32 | 4. (|X| = 1) If X > 0, return 0. Other
33 |
34 | 5. (|X| > 1) Generate an invalid opera
35 | Exit.
36 |
37
38 | Copyright (C) Motorola, Inc. 1
39 | All Rights Reserved
40 |
41 | For details on the license for this fi
42 | file, README, in this same directory.
43
44 |SACOS idnt 2,1 | Motorola 040 Floating Po
45
46 |section 8
47
48 PI: .long 0x40000000,0xC90FDAA2,0x2168C235
49 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235
50
51 |xref t_operr
52 |xref t_frcinx
53 |xref satan
54
55 .global sacosd
56 sacosd:
57 |--ACOS(X) = PI/2 FOR DENORMALIZED X
58 fmovel %d1,%fpcr
59 fmovex PIBY2,%fp0
60 bra t_frcinx
61
62 .global sacos
63 sacos:
64 fmovex (%a0),%fp0 | ...L
65
66 movel (%a0),%d0
67 movew 4(%a0),%d0
68 andil #0x7FFFFFFF,%d0
69 cmpil #0x3FFF8000,%d0
70 bges ACOSBIG
71
72 |--THIS IS THE USUAL CASE, |X| < 1
73 |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) )
74
75 fmoves #0x3F800000,%fp1
76 faddx %fp0,%fp1
77 fnegx %fp0 | ...
78 fadds #0x3F800000,%fp0
79 fdivx %fp1,%fp0
80 fsqrtx %fp0 | ...S
81 fmovemx %fp0-%fp0,(%a0) | ...overwrite
82 movel %d1,-(%sp) |save
83 clrl %d1
84 bsr satan | ...A
85 fmovel (%sp)+,%fpcr |resto
86 faddx %fp0,%fp0
87 bra t_frcinx
88
89 ACOSBIG:
90 fabsx %fp0
91 fcmps #0x3F800000,%fp0
92 fbgt t_operr |cause
93
94 |--|X| = 1, ACOS(X) = 0 OR PI
95 movel (%a0),%d0
96 movew 4(%a0),%d0
97 cmpl #0,%d0 |D0 ha
98 bgts ACOSP1
99
100 |--X = -1
101 |Returns PI and inexact exception
102 fmovex PI,%fp0
103 fmovel %d1,%FPCR
104 fadds #0x00800000,%fp0
105 | ;into
106 | ;fp in
107 bra t_frcinx
108
109 ACOSP1:
110 fmovel %d1,%FPCR
111 fmoves #0x00000000,%fp0
112 rts |Facos
113
114 |end
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