```   1|
2|       scosh.sa 3.1 12/10/90
3|
4|       The entry point sCosh computes the hyperbolic cosine of
5|       an input argument; sCoshd does the same except for denormalized
6|       input.
7|
8|       Input: Double-extended number X in location pointed to
10|
11|       Output: The value cosh(X) returned in floating-point register Fp0.
12|
13|       Accuracy and Monotonicity: The returned result is within 3 ulps in
14|               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15|               result is subsequently rounded to double precision. The
16|               result is provably monotonic in double precision.
17|
18|       Speed: The program sCOSH takes approximately 250 cycles.
19|
20|       Algorithm:
21|
22|       COSH
23|       1. If |X| > 16380 log2, go to 3.
24|
25|       2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
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 log2, go to 5.
31|
32|       4. (16380 log2 < |X| <= 16480 log2)
33|               cosh(X) = sign(X) * exp(|X|)/2.
34|               However, invoking exp(|X|) may cause premature overflow.
35|               Thus, we calculate sinh(X) as follows:
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 overflow. Return
43|               Huge*Huge to generate overflow and an infinity with
44|               the appropriate sign. Huge is the largest finite number in
45|               extended format. Exit.
46|
47|
48
49|               Copyright (C) Motorola, Inc. 1990
51|
52|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
53|       The copyright notice above does not evidence any
54|       actual or intended publication of such source code.
55
56|SCOSH  idnt    2,1 | Motorola 040 Floating Point Software Package
57
58        |section        8
59
60        |xref   t_ovfl
61        |xref   t_frcinx
62        |xref   setox
63
64T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
65T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
66
67TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
68
69        .global scoshd
70scoshd:
71|--COSH(X) = 1 FOR DENORMALIZED X
72
73        fmoves          #0x3F800000,%fp0
74
75        fmovel          %d1,%FPCR
77        bra             t_frcinx
78
79        .global scosh
80scosh:
81        fmovex          (%a0),%fp0      | ...LOAD INPUT
82
83        movel           (%a0),%d0
84        movew           4(%a0),%d0
85        andil           #0x7FFFFFFF,%d0
86        cmpil           #0x400CB167,%d0
87        bgts            COSHBIG
88
89|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
90|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
91
92        fabsx           %fp0            | ...|X|
93
94        movel           %d1,-(%sp)
95        clrl            %d1
96        fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
97        bsr             setox           | ...FP0 IS EXP(|X|)
98        fmuls           #0x3F000000,%fp0        | ...(1/2)EXP(|X|)
99        movel           (%sp)+,%d1
100
101        fmoves          #0x3E800000,%fp1        | ...(1/4)
102        fdivx           %fp0,%fp1               | ...1/(2 EXP(|X|))
103
104        fmovel          %d1,%FPCR
106
107        bra             t_frcinx
108
109COSHBIG:
110        cmpil           #0x400CB2B3,%d0
111        bgts            COSHHUGE
112
113        fabsx           %fp0
115        fsubd           T2(%pc),%fp0            | ...|X| - 16381 LOG2, ACCURATE
116
117        movel           %d1,-(%sp)
118        clrl            %d1
119        fmovemx %fp0-%fp0,(%a0)
120        bsr             setox
121        fmovel          (%sp)+,%fpcr
122
123        fmulx           TWO16380(%pc),%fp0
124        bra             t_frcinx
125
126COSHHUGE:
127        fmovel          #0,%fpsr                |clr N bit if set by source
128        bclrb           #7,(%a0)                |always return positive value
129        fmovemx (%a0),%fp0-%fp0
130        bra             t_ovfl
131
132        |end
133```
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