1 | 1 |
2 | sacos.sa 3.3 12/19/90 2 | sacos.sa 3.3 12/19/90
3 | 3 |
4 | Description: The entry point sAcos com 4 | Description: The entry point sAcos computes the inverse cosine of
5 | an input argument; sAcosd does 5 | an input argument; sAcosd does the same except for denormalized
6 | input. 6 | input.
7 | 7 |
8 | Input: Double-extended number X in loc 8 | Input: Double-extended number X in location pointed to
9 | by address register a0. 9 | by address register a0.
10 | 10 |
11 | Output: The value arccos(X) returned i 11 | Output: The value arccos(X) returned in floating-point register Fp0.
12 | 12 |
13 | Accuracy and Monotonicity: The returne 13 | Accuracy and Monotonicity: The returned result is within 3 ulps in
14 | 64 significant bit, i.e. withi 14 | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15 | result is subsequently rounded 15 | result is subsequently rounded to double precision. The
16 | result is provably monotonic i 16 | result is provably monotonic in double precision.
17 | 17 |
18 | Speed: The program sCOS takes approxim 18 | Speed: The program sCOS takes approximately 310 cycles.
19 | 19 |
20 | Algorithm: 20 | Algorithm:
21 | 21 |
22 | ACOS 22 | ACOS
23 | 1. If |X| >= 1, go to 3. 23 | 1. If |X| >= 1, go to 3.
24 | 24 |
25 | 2. (|X| < 1) Calculate acos(X) by 25 | 2. (|X| < 1) Calculate acos(X) by
26 | z := (1-X) / (1+X) 26 | z := (1-X) / (1+X)
27 | acos(X) = 2 * atan( sqrt(z) ). 27 | acos(X) = 2 * atan( sqrt(z) ).
28 | Exit. 28 | Exit.
29 | 29 |
30 | 3. If |X| > 1, go to 5. 30 | 3. If |X| > 1, go to 5.
31 | 31 |
32 | 4. (|X| = 1) If X > 0, return 0. Other 32 | 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
33 | 33 |
34 | 5. (|X| > 1) Generate an invalid opera 34 | 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
35 | Exit. 35 | Exit.
36 | 36 |
37 37
38 | Copyright (C) Motorola, Inc. 1 38 | Copyright (C) Motorola, Inc. 1990
39 | All Rights Reserved 39 | All Rights Reserved
40 | 40 |
41 | For details on the license for this fi 41 | For details on the license for this file, please see the
42 | file, README, in this same directory. 42 | file, README, in this same directory.
43 43
44 |SACOS idnt 2,1 | Motorola 040 Floating Po 44 |SACOS idnt 2,1 | Motorola 040 Floating Point Software Package
45 45
46 |section 8 46 |section 8
47 47
48 PI: .long 0x40000000,0xC90FDAA2,0x2168C235 48 PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
49 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235 49 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
50 50
51 |xref t_operr 51 |xref t_operr
52 |xref t_frcinx 52 |xref t_frcinx
53 |xref satan 53 |xref satan
54 54
55 .global sacosd 55 .global sacosd
56 sacosd: 56 sacosd:
57 |--ACOS(X) = PI/2 FOR DENORMALIZED X 57 |--ACOS(X) = PI/2 FOR DENORMALIZED X
58 fmovel %d1,%fpcr 58 fmovel %d1,%fpcr | ...load user's rounding mode/precision
59 fmovex PIBY2,%fp0 59 fmovex PIBY2,%fp0
60 bra t_frcinx 60 bra t_frcinx
61 61
62 .global sacos 62 .global sacos
63 sacos: 63 sacos:
64 fmovex (%a0),%fp0 | ...L 64 fmovex (%a0),%fp0 | ...LOAD INPUT
65 65
66 movel (%a0),%d0 66 movel (%a0),%d0 | ...pack exponent with upper 16 fraction
67 movew 4(%a0),%d0 67 movew 4(%a0),%d0
68 andil #0x7FFFFFFF,%d0 68 andil #0x7FFFFFFF,%d0
69 cmpil #0x3FFF8000,%d0 69 cmpil #0x3FFF8000,%d0
70 bges ACOSBIG 70 bges ACOSBIG
71 71
72 |--THIS IS THE USUAL CASE, |X| < 1 72 |--THIS IS THE USUAL CASE, |X| < 1
73 |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) 73 |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
74 74
75 fmoves #0x3F800000,%fp1 75 fmoves #0x3F800000,%fp1
76 faddx %fp0,%fp1 76 faddx %fp0,%fp1 | ...1+X
77 fnegx %fp0 | ... 77 fnegx %fp0 | ... -X
78 fadds #0x3F800000,%fp0 78 fadds #0x3F800000,%fp0 | ...1-X
79 fdivx %fp1,%fp0 79 fdivx %fp1,%fp0 | ...(1-X)/(1+X)
80 fsqrtx %fp0 | ...S 80 fsqrtx %fp0 | ...SQRT((1-X)/(1+X))
81 fmovemx %fp0-%fp0,(%a0) | ...overwrite 81 fmovemx %fp0-%fp0,(%a0) | ...overwrite input
82 movel %d1,-(%sp) |save 82 movel %d1,-(%sp) |save original users fpcr
83 clrl %d1 83 clrl %d1
84 bsr satan | ...A 84 bsr satan | ...ATAN(SQRT([1-X]/[1+X]))
85 fmovel (%sp)+,%fpcr |resto 85 fmovel (%sp)+,%fpcr |restore users exceptions
86 faddx %fp0,%fp0 86 faddx %fp0,%fp0 | ...2 * ATAN( STUFF )
87 bra t_frcinx 87 bra t_frcinx
88 88
89 ACOSBIG: 89 ACOSBIG:
90 fabsx %fp0 90 fabsx %fp0
91 fcmps #0x3F800000,%fp0 91 fcmps #0x3F800000,%fp0
92 fbgt t_operr |cause 92 fbgt t_operr |cause an operr exception
93 93
94 |--|X| = 1, ACOS(X) = 0 OR PI 94 |--|X| = 1, ACOS(X) = 0 OR PI
95 movel (%a0),%d0 95 movel (%a0),%d0 | ...pack exponent with upper 16 fraction
96 movew 4(%a0),%d0 96 movew 4(%a0),%d0
97 cmpl #0,%d0 |D0 ha 97 cmpl #0,%d0 |D0 has original exponent+fraction
98 bgts ACOSP1 98 bgts ACOSP1
99 99
100 |--X = -1 100 |--X = -1
101 |Returns PI and inexact exception 101 |Returns PI and inexact exception
102 fmovex PI,%fp0 102 fmovex PI,%fp0
103 fmovel %d1,%FPCR 103 fmovel %d1,%FPCR
104 fadds #0x00800000,%fp0 104 fadds #0x00800000,%fp0 |cause an inexact exception to be put
105 | ;into 105 | ;into the 040 - will not trap until next
106 | ;fp in 106 | ;fp inst.
107 bra t_frcinx 107 bra t_frcinx
108 108
109 ACOSP1: 109 ACOSP1:
110 fmovel %d1,%FPCR 110 fmovel %d1,%FPCR
111 fmoves #0x00000000,%fp0 111 fmoves #0x00000000,%fp0
112 rts |Facos 112 rts |Facos ; of +1 is exact
113 113
114 |end 114 |end
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