1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
|
| scosh.sa 3.1 12/10/90
|
| The entry point sCosh computes the hyperbolic cosine of
| an input argument; sCoshd does the same except for denormalized
| input.
|
| Input: Double-extended number X in location pointed to
| by address register a0.
|
| Output: The value cosh(X) returned in floating-point register Fp0.
|
| Accuracy and Monotonicity: The returned result is within 3 ulps in
| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
| result is subsequently rounded to double precision. The
| result is provably monotonic in double precision.
|
| Speed: The program sCOSH takes approximately 250 cycles.
|
| Algorithm:
|
| COSH
| 1. If |X| > 16380 log2, go to 3.
|
| 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
| y = |X|, z = exp(Y), and
| cosh(X) = (1/2)*( z + 1/z ).
| Exit.
|
| 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
|
| 4. (16380 log2 < |X| <= 16480 log2)
| cosh(X) = sign(X) * exp(|X|)/2.
| However, invoking exp(|X|) may cause premature overflow.
| Thus, we calculate sinh(X) as follows:
| Y := |X|
| Fact := 2**(16380)
| Y' := Y - 16381 log2
| cosh(X) := Fact * exp(Y').
| Exit.
|
| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
| Huge*Huge to generate overflow and an infinity with
| the appropriate sign. Huge is the largest finite number in
| extended format. Exit.
|
|
| Copyright (C) Motorola, Inc. 1990
| All Rights Reserved
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
|xref t_ovfl
|xref t_frcinx
|xref setox
T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
.global scoshd
scoshd:
|--COSH(X) = 1 FOR DENORMALIZED X
fmoves #0x3F800000,%fp0
fmovel %d1,%FPCR
fadds #0x00800000,%fp0
bra t_frcinx
.global scosh
scosh:
fmovex (%a0),%fp0 | ...LOAD INPUT
movel (%a0),%d0
movew 4(%a0),%d0
andil #0x7FFFFFFF,%d0
cmpil #0x400CB167,%d0
bgts COSHBIG
|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
fabsx %fp0 | ...|X|
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
bsr setox | ...FP0 IS EXP(|X|)
fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|)
movel (%sp)+,%d1
fmoves #0x3E800000,%fp1 | ...(1/4)
fdivx %fp0,%fp1 | ...1/(2 EXP(|X|))
fmovel %d1,%FPCR
faddx %fp1,%fp0
bra t_frcinx
COSHBIG:
cmpil #0x400CB2B3,%d0
bgts COSHHUGE
fabsx %fp0
fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0)
bsr setox
fmovel (%sp)+,%fpcr
fmulx TWO16380(%pc),%fp0
bra t_frcinx
COSHHUGE:
fmovel #0,%fpsr |clr N bit if set by source
bclrb #7,(%a0) |always return positive value
fmovemx (%a0),%fp0-%fp0
bra t_ovfl
|end
|
