1 |
2 | sasin.sa 3.3 12/19/90
3 |
4 | Description: The entry point sAsin com
5 | an input argument; sAsind does
6 | input.
7 |
8 | Input: Double-extended number X in loc
9 | by address register a0.
10 |
11 | Output: The value arcsin(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 sASIN takes approxi
19 |
20 | Algorithm:
21 |
22 | ASIN
23 | 1. If |X| >= 1, go to 3.
24 |
25 | 2. (|X| < 1) Calculate asin(X) by
26 | z := sqrt( [1-X][1+X] )
27 | asin(X) = atan( x / z ).
28 | Exit.
29 |
30 | 3. If |X| > 1, go to 5.
31 |
32 | 4. (|X| = 1) sgn := sign(X), return as
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 |SASIN idnt 2,1 | Motorola 040 Floating Po
45
46 |section 8
47
48 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235
49
50 |xref t_operr
51 |xref t_frcinx
52 |xref t_extdnrm
53 |xref satan
54
55 .global sasind
56 sasind:
57 |--ASIN(X) = X FOR DENORMALIZED X
58
59 bra t_extdnrm
60
61 .global sasin
62 sasin:
63 fmovex (%a0),%fp0 | ...L
64
65 movel (%a0),%d0
66 movew 4(%a0),%d0
67 andil #0x7FFFFFFF,%d0
68 cmpil #0x3FFF8000,%d0
69 bges asinbig
70
71 |--THIS IS THE USUAL CASE, |X| < 1
72 |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
73
74 fmoves #0x3F800000,%fp1
75 fsubx %fp0,%fp1
76 fmovemx %fp2-%fp2,-(%a7)
77 fmoves #0x3F800000,%fp2
78 faddx %fp0,%fp2
79 fmulx %fp2,%fp1
80 fmovemx (%a7)+,%fp2-%fp2
81 fsqrtx %fp1 | ...S
82 fdivx %fp1,%fp0
83 fmovemx %fp0-%fp0,(%a0)
84 bsr satan
85 bra t_frcinx
86
87 asinbig:
88 fabsx %fp0 | ...|X|
89 fcmps #0x3F800000,%fp0
90 fbgt t_operr |cause
91
92 |--|X| = 1, ASIN(X) = +- PI/2.
93
94 fmovex PIBY2,%fp0
95 movel (%a0),%d0
96 andil #0x80000000,%d0 | ...S
97 oril #0x3F800000,%d0 | ...+
98 movel %d0,-(%sp) | ...p
99 fmovel %d1,%FPCR
100 fmuls (%sp)+,%fp0
101 bra t_frcinx
102
103 |end
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