1 |
2 | scosh.sa 3.1 12/10/90
3 |
4 | The entry point sCosh computes the hyp
5 | an input argument; sCoshd does the sam
6 | input.
7 |
8 | Input: Double-extended number X in loc
9 | by address register a0.
10 |
11 | Output: The value cosh(X) returned in
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 sCOSH takes approxi
19 |
20 | Algorithm:
21 |
22 | COSH
23 | 1. If |X| > 16380 log2, go to 3.
24 |
25 | 2. (|X| <= 16380 log2) Cosh(X) is obta
26 | y = |X|, z = exp(Y), and
27 | cosh(X) = (1/2)*( z + 1/z ).
28 | Exit.
29 |
30 | 3. (|X| > 16380 log2). If |X| > 16480
31 |
32 | 4. (16380 log2 < |X| <= 16480 log2)
33 | cosh(X) = sign(X) * exp(|X|)/2
34 | However, invoking exp(|X|) may
35 | Thus, we calculate sinh(X) as
36 | Y := |X|
37 | Fact := 2**(16380)
38 | Y' := Y - 16381 log2
39 | cosh(X) := Fact * exp(Y').
40 | Exit.
41 |
42 | 5. (|X| > 16480 log2) sinh(X) must ove
43 | Huge*Huge to generate overflow
44 | the appropriate sign. Huge is
45 | extended format. Exit.
46 |
47 |
48
49 | Copyright (C) Motorola, Inc. 1
50 | All Rights Reserved
51 |
52 | For details on the license for this fi
53 | file, README, in this same directory.
54
55 |SCOSH idnt 2,1 | Motorola 040 Floating Po
56
57 |section 8
58
59 |xref t_ovfl
60 |xref t_frcinx
61 |xref setox
62
63 T1: .long 0x40C62D38,0xD3D64634 | ... 1638
64 T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 1638
65
66 TWO16380: .long 0x7FFB0000,0x80000000,0x000000
67
68 .global scoshd
69 scoshd:
70 |--COSH(X) = 1 FOR DENORMALIZED X
71
72 fmoves #0x3F800000,%fp0
73
74 fmovel %d1,%FPCR
75 fadds #0x00800000,%fp0
76 bra t_frcinx
77
78 .global scosh
79 scosh:
80 fmovex (%a0),%fp0 | ...L
81
82 movel (%a0),%d0
83 movew 4(%a0),%d0
84 andil #0x7FFFFFFF,%d0
85 cmpil #0x400CB167,%d0
86 bgts COSHBIG
87
88 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
89 |--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
90
91 fabsx %fp0 | ...|
92
93 movel %d1,-(%sp)
94 clrl %d1
95 fmovemx %fp0-%fp0,(%a0) |pass paramete
96 bsr setox | ...F
97 fmuls #0x3F000000,%fp0
98 movel (%sp)+,%d1
99
100 fmoves #0x3E800000,%fp1
101 fdivx %fp0,%fp1
102
103 fmovel %d1,%FPCR
104 faddx %fp1,%fp0
105
106 bra t_frcinx
107
108 COSHBIG:
109 cmpil #0x400CB2B3,%d0
110 bgts COSHHUGE
111
112 fabsx %fp0
113 fsubd T1(%pc),%fp0
114 fsubd T2(%pc),%fp0
115
116 movel %d1,-(%sp)
117 clrl %d1
118 fmovemx %fp0-%fp0,(%a0)
119 bsr setox
120 fmovel (%sp)+,%fpcr
121
122 fmulx TWO16380(%pc),%fp0
123 bra t_frcinx
124
125 COSHHUGE:
126 fmovel #0,%fpsr
127 bclrb #7,(%a0)
128 fmovemx (%a0),%fp0-%fp0
129 bra t_ovfl
130
131 |end
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