1|
2|	sasin.sa 3.3 12/19/90
3|
4|	Description: The entry point sAsin computes the inverse sine of
5|		an input argument; sAsind 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 arcsin(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 sASIN takes approximately 310 cycles.
19|
20|	Algorithm:
21|
22|	ASIN
23|	1. If |X| >= 1, go to 3.
24|
25|	2. (|X| < 1) Calculate asin(X) by
26|		z := sqrt( [1-X][1+X] )
27|		asin(X) = atan( x / z ).
28|		Exit.
29|
30|	3. If |X| > 1, go to 5.
31|
32|	4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. 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|SASIN	idnt	2,1 | Motorola 040 Floating Point Software Package
45
46	|section	8
47
48PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
49
50	|xref	t_operr
51	|xref	t_frcinx
52	|xref	t_extdnrm
53	|xref	satan
54
55	.global	sasind
56sasind:
57|--ASIN(X) = X FOR DENORMALIZED X
58
59	bra		t_extdnrm
60
61	.global	sasin
62sasin:
63	fmovex		(%a0),%fp0	| ...LOAD INPUT
64
65	movel		(%a0),%d0
66	movew		4(%a0),%d0
67	andil		#0x7FFFFFFF,%d0
68	cmpil		#0x3FFF8000,%d0
69	bges		asinbig
70
71|--THIS IS THE USUAL CASE, |X| < 1
72|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
73
74	fmoves		#0x3F800000,%fp1
75	fsubx		%fp0,%fp1		| ...1-X
76	fmovemx	%fp2-%fp2,-(%a7)
77	fmoves		#0x3F800000,%fp2
78	faddx		%fp0,%fp2		| ...1+X
79	fmulx		%fp2,%fp1		| ...(1+X)(1-X)
80	fmovemx	(%a7)+,%fp2-%fp2
81	fsqrtx		%fp1		| ...SQRT([1-X][1+X])
82	fdivx		%fp1,%fp0		| ...X/SQRT([1-X][1+X])
83	fmovemx	%fp0-%fp0,(%a0)
84	bsr		satan
85	bra		t_frcinx
86
87asinbig:
88	fabsx		%fp0	 | ...|X|
89	fcmps		#0x3F800000,%fp0
90	fbgt		t_operr		|cause an operr exception
91
92|--|X| = 1, ASIN(X) = +- PI/2.
93
94	fmovex		PIBY2,%fp0
95	movel		(%a0),%d0
96	andil		#0x80000000,%d0	| ...SIGN BIT OF X
97	oril		#0x3F800000,%d0	| ...+-1 IN SGL FORMAT
98	movel		%d0,-(%sp)	| ...push SIGN(X) IN SGL-FMT
99	fmovel		%d1,%FPCR
100	fmuls		(%sp)+,%fp0
101	bra		t_frcinx
102
103	|end
104