1|
2|	sacos.sa 3.3 12/19/90
3|
4|	Description: The entry point sAcos computes the inverse cosine of
5|		an input argument; sAcosd 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 arccos(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 sCOS takes approximately 310 cycles.
19|
20|	Algorithm:
21|
22|	ACOS
23|	1. If |X| >= 1, go to 3.
24|
25|	2. (|X| < 1) Calculate acos(X) by
26|		z := (1-X) / (1+X)
27|		acos(X) = 2 * atan( sqrt(z) ).
28|		Exit.
29|
30|	3. If |X| > 1, go to 5.
31|
32|	4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
33|
34|	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
35|		Exit.
36|
37
38|		Copyright (C) Motorola, Inc. 1990
39|			All Rights Reserved
40|
41|       For details on the license for this file, please see the
42|       file, README, in this same directory.
43
44|SACOS	idnt	2,1 | Motorola 040 Floating Point Software Package
45
46	|section	8
47
48PI:	.long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
49PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
50
51	|xref	t_operr
52	|xref	t_frcinx
53	|xref	satan
54
55	.global	sacosd
56sacosd:
57|--ACOS(X) = PI/2 FOR DENORMALIZED X
58	fmovel		%d1,%fpcr		| ...load user's rounding mode/precision
59	fmovex		PIBY2,%fp0
60	bra		t_frcinx
61
62	.global	sacos
63sacos:
64	fmovex		(%a0),%fp0	| ...LOAD INPUT
65
66	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction
67	movew		4(%a0),%d0
68	andil		#0x7FFFFFFF,%d0
69	cmpil		#0x3FFF8000,%d0
70	bges		ACOSBIG
71
72|--THIS IS THE USUAL CASE, |X| < 1
73|--ACOS(X) = 2 * ATAN(	SQRT( (1-X)/(1+X) )	)
74
75	fmoves		#0x3F800000,%fp1
76	faddx		%fp0,%fp1		| ...1+X
77	fnegx		%fp0		| ... -X
78	fadds		#0x3F800000,%fp0	| ...1-X
79	fdivx		%fp1,%fp0		| ...(1-X)/(1+X)
80	fsqrtx		%fp0		| ...SQRT((1-X)/(1+X))
81	fmovemx	%fp0-%fp0,(%a0)	| ...overwrite input
82	movel		%d1,-(%sp)	|save original users fpcr
83	clrl		%d1
84	bsr		satan		| ...ATAN(SQRT([1-X]/[1+X]))
85	fmovel		(%sp)+,%fpcr	|restore users exceptions
86	faddx		%fp0,%fp0		| ...2 * ATAN( STUFF )
87	bra		t_frcinx
88
89ACOSBIG:
90	fabsx		%fp0
91	fcmps		#0x3F800000,%fp0
92	fbgt		t_operr		|cause an operr exception
93
94|--|X| = 1, ACOS(X) = 0 OR PI
95	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction
96	movew		4(%a0),%d0
97	cmpl		#0,%d0		|D0 has original exponent+fraction
98	bgts		ACOSP1
99
100|--X = -1
101|Returns PI and inexact exception
102	fmovex		PI,%fp0
103	fmovel		%d1,%FPCR
104	fadds		#0x00800000,%fp0	|cause an inexact exception to be put
105|					;into the 040 - will not trap until next
106|					;fp inst.
107	bra		t_frcinx
108
109ACOSP1:
110	fmovel		%d1,%FPCR
111	fmoves		#0x00000000,%fp0
112	rts				|Facos ; of +1 is exact
113
114	|end
115