1 | 1 |
2 | sasin.sa 3.3 12/19/90 2 | sasin.sa 3.3 12/19/90
3 | 3 |
4 | Description: The entry point sAsin com 4 | Description: The entry point sAsin computes the inverse sine of
5 | an input argument; sAsind does 5 | an input argument; sAsind 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 arcsin(X) returned i 11 | Output: The value arcsin(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 sASIN takes approxi 18 | Speed: The program sASIN takes approximately 310 cycles.
19 | 19 |
20 | Algorithm: 20 | Algorithm:
21 | 21 |
22 | ASIN 22 | ASIN
23 | 1. If |X| >= 1, go to 3. 23 | 1. If |X| >= 1, go to 3.
24 | 24 |
25 | 2. (|X| < 1) Calculate asin(X) by 25 | 2. (|X| < 1) Calculate asin(X) by
26 | z := sqrt( [1-X][1+X] ) 26 | z := sqrt( [1-X][1+X] )
27 | asin(X) = atan( x / z ). 27 | asin(X) = atan( x / 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) sgn := sign(X), return as 32 | 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. 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 |SASIN idnt 2,1 | Motorola 040 Floating Po 44 |SASIN idnt 2,1 | Motorola 040 Floating Point Software Package
45 45
46 |section 8 46 |section 8
47 47
48 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235 48 PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
49 49
50 |xref t_operr 50 |xref t_operr
51 |xref t_frcinx 51 |xref t_frcinx
52 |xref t_extdnrm 52 |xref t_extdnrm
53 |xref satan 53 |xref satan
54 54
55 .global sasind 55 .global sasind
56 sasind: 56 sasind:
57 |--ASIN(X) = X FOR DENORMALIZED X 57 |--ASIN(X) = X FOR DENORMALIZED X
58 58
59 bra t_extdnrm 59 bra t_extdnrm
60 60
61 .global sasin 61 .global sasin
62 sasin: 62 sasin:
63 fmovex (%a0),%fp0 | ...L 63 fmovex (%a0),%fp0 | ...LOAD INPUT
64 64
65 movel (%a0),%d0 65 movel (%a0),%d0
66 movew 4(%a0),%d0 66 movew 4(%a0),%d0
67 andil #0x7FFFFFFF,%d0 67 andil #0x7FFFFFFF,%d0
68 cmpil #0x3FFF8000,%d0 68 cmpil #0x3FFF8000,%d0
69 bges asinbig 69 bges asinbig
70 70
71 |--THIS IS THE USUAL CASE, |X| < 1 71 |--THIS IS THE USUAL CASE, |X| < 1
72 |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) ) 72 |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
73 73
74 fmoves #0x3F800000,%fp1 74 fmoves #0x3F800000,%fp1
75 fsubx %fp0,%fp1 75 fsubx %fp0,%fp1 | ...1-X
76 fmovemx %fp2-%fp2,-(%a7) 76 fmovemx %fp2-%fp2,-(%a7)
77 fmoves #0x3F800000,%fp2 77 fmoves #0x3F800000,%fp2
78 faddx %fp0,%fp2 78 faddx %fp0,%fp2 | ...1+X
79 fmulx %fp2,%fp1 79 fmulx %fp2,%fp1 | ...(1+X)(1-X)
80 fmovemx (%a7)+,%fp2-%fp2 80 fmovemx (%a7)+,%fp2-%fp2
81 fsqrtx %fp1 | ...S 81 fsqrtx %fp1 | ...SQRT([1-X][1+X])
82 fdivx %fp1,%fp0 82 fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X])
83 fmovemx %fp0-%fp0,(%a0) 83 fmovemx %fp0-%fp0,(%a0)
84 bsr satan 84 bsr satan
85 bra t_frcinx 85 bra t_frcinx
86 86
87 asinbig: 87 asinbig:
88 fabsx %fp0 | ...|X| 88 fabsx %fp0 | ...|X|
89 fcmps #0x3F800000,%fp0 89 fcmps #0x3F800000,%fp0
90 fbgt t_operr |cause 90 fbgt t_operr |cause an operr exception
91 91
92 |--|X| = 1, ASIN(X) = +- PI/2. 92 |--|X| = 1, ASIN(X) = +- PI/2.
93 93
94 fmovex PIBY2,%fp0 94 fmovex PIBY2,%fp0
95 movel (%a0),%d0 95 movel (%a0),%d0
96 andil #0x80000000,%d0 | ...S 96 andil #0x80000000,%d0 | ...SIGN BIT OF X
97 oril #0x3F800000,%d0 | ...+ 97 oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT
98 movel %d0,-(%sp) | ...p 98 movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT
99 fmovel %d1,%FPCR 99 fmovel %d1,%FPCR
100 fmuls (%sp)+,%fp0 100 fmuls (%sp)+,%fp0
101 bra t_frcinx 101 bra t_frcinx
102 102
103 |end 103 |end
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