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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
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