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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
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