aboutsummaryrefslogtreecommitdiff
path: root/arch/m68k/fpsp040/scosh.S
blob: e81edbb87642007749d43bd57e5bb59aa164c268 (plain)
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
132
|
|	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
|
|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|	The copyright notice above does not evidence any
|	actual or intended publication of such source code.

|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