1|
2|	satanh.sa 3.3 12/19/90
3|
4|	The entry point satanh computes the inverse
5|	hyperbolic tangent of
6|	an input argument; satanhd does the same except for denormalized
7|	input.
8|
9|	Input: Double-extended number X in location pointed to
10|		by address register a0.
11|
12|	Output: The value arctanh(X) returned in floating-point register Fp0.
13|
14|	Accuracy and Monotonicity: The returned result is within 3 ulps in
15|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
16|		result is subsequently rounded to double precision. The
17|		result is provably monotonic in double precision.
18|
19|	Speed: The program satanh takes approximately 270 cycles.
20|
21|	Algorithm:
22|
23|	ATANH
24|	1. If |X| >= 1, go to 3.
25|
26|	2. (|X| < 1) Calculate atanh(X) by
27|		sgn := sign(X)
28|		y := |X|
29|		z := 2y/(1-y)
30|		atanh(X) := sgn * (1/2) * logp1(z)
31|		Exit.
32|
33|	3. If |X| > 1, go to 5.
34|
35|	4. (|X| = 1) Generate infinity with an appropriate sign and
36|		divide-by-zero by
37|		sgn := sign(X)
38|		atan(X) := sgn / (+0).
39|		Exit.
40|
41|	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
42|		Exit.
43|
44
45|		Copyright (C) Motorola, Inc. 1990
46|			All Rights Reserved
47|
48|       For details on the license for this file, please see the
49|       file, README, in this same directory.
50
51|satanh	idnt	2,1 | Motorola 040 Floating Point Software Package
52
53	|section	8
54
55	|xref	t_dz
56	|xref	t_operr
57	|xref	t_frcinx
58	|xref	t_extdnrm
59	|xref	slognp1
60
61	.global	satanhd
62satanhd:
63|--ATANH(X) = X FOR DENORMALIZED X
64
65	bra		t_extdnrm
66
67	.global	satanh
68satanh:
69	movel		(%a0),%d0
70	movew		4(%a0),%d0
71	andil		#0x7FFFFFFF,%d0
72	cmpil		#0x3FFF8000,%d0
73	bges		ATANHBIG
74
75|--THIS IS THE USUAL CASE, |X| < 1
76|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
77
78	fabsx		(%a0),%fp0	| ...Y = |X|
79	fmovex		%fp0,%fp1
80	fnegx		%fp1		| ...-Y
81	faddx		%fp0,%fp0		| ...2Y
82	fadds		#0x3F800000,%fp1	| ...1-Y
83	fdivx		%fp1,%fp0		| ...2Y/(1-Y)
84	movel		(%a0),%d0
85	andil		#0x80000000,%d0
86	oril		#0x3F000000,%d0	| ...SIGN(X)*HALF
87	movel		%d0,-(%sp)
88
89	fmovemx	%fp0-%fp0,(%a0)	| ...overwrite input
90	movel		%d1,-(%sp)
91	clrl		%d1
92	bsr		slognp1		| ...LOG1P(Z)
93	fmovel		(%sp)+,%fpcr
94	fmuls		(%sp)+,%fp0
95	bra		t_frcinx
96
97ATANHBIG:
98	fabsx		(%a0),%fp0	| ...|X|
99	fcmps		#0x3F800000,%fp0
100	fbgt		t_operr
101	bra		t_dz
102
103	|end
104