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
9|		by address register a0.
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
50|			All Rights Reserved
51|
52|       For details on the license for this file, please see the
53|       file, README, in this same directory.
54
55|SCOSH	idnt	2,1 | Motorola 040 Floating Point Software Package
56
57	|section	8
58
59	|xref	t_ovfl
60	|xref	t_frcinx
61	|xref	setox
62
63T1:	.long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
64T2:	.long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
65
66TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
67
68	.global	scoshd
69scoshd:
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
79scosh:
80	fmovex		(%a0),%fp0	| ...LOAD INPUT
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		| ...|X|
92
93	movel		%d1,-(%sp)
94	clrl		%d1
95	fmovemx	%fp0-%fp0,(%a0)	|pass parameter to setox
96	bsr		setox		| ...FP0 IS EXP(|X|)
97	fmuls		#0x3F000000,%fp0	| ...(1/2)EXP(|X|)
98	movel		(%sp)+,%d1
99
100	fmoves		#0x3E800000,%fp1	| ...(1/4)
101	fdivx		%fp0,%fp1		| ...1/(2 EXP(|X|))
102
103	fmovel		%d1,%FPCR
104	faddx		%fp1,%fp0
105
106	bra		t_frcinx
107
108COSHBIG:
109	cmpil		#0x400CB2B3,%d0
110	bgts		COSHHUGE
111
112	fabsx		%fp0
113	fsubd		T1(%pc),%fp0		| ...(|X|-16381LOG2_LEAD)
114	fsubd		T2(%pc),%fp0		| ...|X| - 16381 LOG2, ACCURATE
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
125COSHHUGE:
126	fmovel		#0,%fpsr		|clr N bit if set by source
127	bclrb		#7,(%a0)		|always return positive value
128	fmovemx	(%a0),%fp0-%fp0
129	bra		t_ovfl
130
131	|end
132