1 |
2 | ssinh.sa 3.1 12/10/90
3 |
4 | The entry point sSinh computes the hyp
5 | an input argument; sSinhd does the sam
6 | input.
7 |
8 | Input: Double-extended number X in loc
9 | by address register a0.
10 |
11 | Output: The value sinh(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 sSINH takes approxi
19 |
20 | Algorithm:
21 |
22 | SINH
23 | 1. If |X| > 16380 log2, go to 3.
24 |
25 | 2. (|X| <= 16380 log2) Sinh(X) is obta
26 | y = |X|, sgn = sign(X), and z
27 | sinh(X) = sgn*(1/2)*( z + z/(1
28 | Exit.
29 |
30 | 3. If |X| > 16480 log2, go to 5.
31 |
32 | 4. (16380 log2 < |X| <= 16480 log2)
33 | sinh(X) = sign(X) * exp(|X|)/2
34 | However, invoking exp(|X|) may caus
35 | Thus, we calculate sinh(X) as follo
36 | Y := |X|
37 | sgn := sign(X)
38 | sgnFact := sgn * 2**(16380)
39 | Y' := Y - 16381 log2
40 | sinh(X) := sgnFact * exp(Y').
41 | Exit.
42 |
43 | 5. (|X| > 16480 log2) sinh(X) must ove
44 | sign(X)*Huge*Huge to generate overf
45 | the appropriate sign. Huge is the l
46 | extended format. Exit.
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 |SSINH idnt 2,1 | Motorola 040 Floating Po
56
57 |section 8
58
59 T1: .long 0x40C62D38,0xD3D64634 | ... 1638
60 T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 1638
61
62 |xref t_frcinx
63 |xref t_ovfl
64 |xref t_extdnrm
65 |xref setox
66 |xref setoxm1
67
68 .global ssinhd
69 ssinhd:
70 |--SINH(X) = X FOR DENORMALIZED X
71
72 bra t_extdnrm
73
74 .global ssinh
75 ssinh:
76 fmovex (%a0),%fp0 | ...LOAD INPU
77
78 movel (%a0),%d0
79 movew 4(%a0),%d0
80 movel %d0,%a1 | save a copy
81 andl #0x7FFFFFFF,%d0
82 cmpl #0x400CB167,%d0
83 bgts SINHBIG
84
85 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
86 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1
87
88 fabsx %fp0 | ...Y = |X|
89
90 moveml %a1/%d1,-(%sp)
91 fmovemx %fp0-%fp0,(%a0)
92 clrl %d1
93 bsr setoxm1 | ...FP0 IS Z
94 fmovel #0,%fpcr
95 moveml (%sp)+,%a1/%d1
96
97 fmovex %fp0,%fp1
98 fadds #0x3F800000,%fp1 | ...1
99 fmovex %fp0,-(%sp)
100 fdivx %fp1,%fp0 | ...Z
101 movel %a1,%d0
102 andl #0x80000000,%d0
103 orl #0x3F000000,%d0
104 faddx (%sp)+,%fp0
105 movel %d0,-(%sp)
106
107 fmovel %d1,%fpcr
108 fmuls (%sp)+,%fp0 |last fp inst
109
110 bra t_frcinx
111
112 SINHBIG:
113 cmpl #0x400CB2B3,%d0
114 bgt t_ovfl
115 fabsx %fp0
116 fsubd T1(%pc),%fp0 | ...(|X|-1638
117 movel #0,-(%sp)
118 movel #0x80000000,-(%sp)
119 movel %a1,%d0
120 andl #0x80000000,%d0
121 orl #0x7FFB0000,%d0
122 movel %d0,-(%sp) | ...EXTENDED
123 fsubd T2(%pc),%fp0 | ...|X| - 163
124
125 movel %d1,-(%sp)
126 clrl %d1
127 fmovemx %fp0-%fp0,(%a0)
128 bsr setox
129 fmovel (%sp)+,%fpcr
130
131 fmulx (%sp)+,%fp0 |possible exce
132 bra t_frcinx
133
134 |end
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