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1da177e4 LT |
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 | | | |
e00d82d0 MW |
41 | | For details on the license for this file, please see the |
42 | | file, README, in this same directory. | |
1da177e4 LT |
43 | |
44 | |SASIN idnt 2,1 | Motorola 040 Floating Point Software Package | |
45 | ||
46 | |section 8 | |
47 | ||
48 | PIBY2: .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 | |
56 | sasind: | |
57 | |--ASIN(X) = X FOR DENORMALIZED X | |
58 | ||
59 | bra t_extdnrm | |
60 | ||
61 | .global sasin | |
62 | sasin: | |
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 | ||
87 | asinbig: | |
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 |