1 |
2 | satanh.sa 3.3 12/19/90
3 |
4 | The entry point satanh computes the in
5 | hyperbolic tangent of
6 | an input argument; satanhd does the sa
7 | input.
8 |
9 | Input: Double-extended number X in loc
10 | by address register a0.
11 |
12 | Output: The value arctanh(X) returned
13 |
14 | Accuracy and Monotonicity: The returne
15 | 64 significant bit, i.e. withi
16 | result is subsequently rounded
17 | result is provably monotonic i
18 |
19 | Speed: The program satanh takes approx
20 |
21 | Algorithm:
22 |
23 | ATANH
24 | 1. If |X| >= 1, go to 3.
25 |
26 | 2. (|X| < 1) Calculate atanh(X) by
27 | sgn := sign(X)
28 | y := |X|
29 | z := 2y/(1-y)
30 | atanh(X) := sgn * (1/2) * logp
31 | Exit.
32 |
33 | 3. If |X| > 1, go to 5.
34 |
35 | 4. (|X| = 1) Generate infinity with an
36 | divide-by-zero by
37 | sgn := sign(X)
38 | atan(X) := sgn / (+0).
39 | Exit.
40 |
41 | 5. (|X| > 1) Generate an invalid opera
42 | Exit.
43 |
44
45 | Copyright (C) Motorola, Inc. 1
46 | All Rights Reserved
47 |
48 | For details on the license for this fi
49 | file, README, in this same directory.
50
51 |satanh idnt 2,1 | Motorola 040 Floating Po
52
53 |section 8
54
55 |xref t_dz
56 |xref t_operr
57 |xref t_frcinx
58 |xref t_extdnrm
59 |xref slognp1
60
61 .global satanhd
62 satanhd:
63 |--ATANH(X) = X FOR DENORMALIZED X
64
65 bra t_extdnrm
66
67 .global satanh
68 satanh:
69 movel (%a0),%d0
70 movew 4(%a0),%d0
71 andil #0x7FFFFFFF,%d0
72 cmpil #0x3FFF8000,%d0
73 bges ATANHBIG
74
75 |--THIS IS THE USUAL CASE, |X| < 1
76 |--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) *
77
78 fabsx (%a0),%fp0 | ...Y
79 fmovex %fp0,%fp1
80 fnegx %fp1 | ...-
81 faddx %fp0,%fp0
82 fadds #0x3F800000,%fp1
83 fdivx %fp1,%fp0
84 movel (%a0),%d0
85 andil #0x80000000,%d0
86 oril #0x3F000000,%d0 | ...S
87 movel %d0,-(%sp)
88
89 fmovemx %fp0-%fp0,(%a0) | ...overwrite
90 movel %d1,-(%sp)
91 clrl %d1
92 bsr slognp1 | ...L
93 fmovel (%sp)+,%fpcr
94 fmuls (%sp)+,%fp0
95 bra t_frcinx
96
97 ATANHBIG:
98 fabsx (%a0),%fp0 | ...|
99 fcmps #0x3F800000,%fp0
100 fbgt t_operr
101 bra t_dz
102
103 |end
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