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Diffstat (limited to 'arch/m68k/fpsp040/sacos.S')
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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41 | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | ||
42 | | The copyright notice above does not evidence any | ||
43 | | actual or intended publication of such source code. | ||
44 | |||
45 | |SACOS idnt 2,1 | Motorola 040 Floating Point Software Package | ||
46 | |||
47 | |section 8 | ||
48 | |||
49 | PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000 | ||
50 | PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 | ||
51 | |||
52 | |xref t_operr | ||
53 | |xref t_frcinx | ||
54 | |xref satan | ||
55 | |||
56 | .global sacosd | ||
57 | sacosd: | ||
58 | |--ACOS(X) = PI/2 FOR DENORMALIZED X | ||
59 | fmovel %d1,%fpcr | ...load user's rounding mode/precision | ||
60 | fmovex PIBY2,%fp0 | ||
61 | bra t_frcinx | ||
62 | |||
63 | .global sacos | ||
64 | sacos: | ||
65 | fmovex (%a0),%fp0 | ...LOAD INPUT | ||
66 | |||
67 | movel (%a0),%d0 | ...pack exponent with upper 16 fraction | ||
68 | movew 4(%a0),%d0 | ||
69 | andil #0x7FFFFFFF,%d0 | ||
70 | cmpil #0x3FFF8000,%d0 | ||
71 | bges ACOSBIG | ||
72 | |||
73 | |--THIS IS THE USUAL CASE, |X| < 1 | ||
74 | |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) ) | ||
75 | |||
76 | fmoves #0x3F800000,%fp1 | ||
77 | faddx %fp0,%fp1 | ...1+X | ||
78 | fnegx %fp0 | ... -X | ||
79 | fadds #0x3F800000,%fp0 | ...1-X | ||
80 | fdivx %fp1,%fp0 | ...(1-X)/(1+X) | ||
81 | fsqrtx %fp0 | ...SQRT((1-X)/(1+X)) | ||
82 | fmovemx %fp0-%fp0,(%a0) | ...overwrite input | ||
83 | movel %d1,-(%sp) |save original users fpcr | ||
84 | clrl %d1 | ||
85 | bsr satan | ...ATAN(SQRT([1-X]/[1+X])) | ||
86 | fmovel (%sp)+,%fpcr |restore users exceptions | ||
87 | faddx %fp0,%fp0 | ...2 * ATAN( STUFF ) | ||
88 | bra t_frcinx | ||
89 | |||
90 | ACOSBIG: | ||
91 | fabsx %fp0 | ||
92 | fcmps #0x3F800000,%fp0 | ||
93 | fbgt t_operr |cause an operr exception | ||
94 | |||
95 | |--|X| = 1, ACOS(X) = 0 OR PI | ||
96 | movel (%a0),%d0 | ...pack exponent with upper 16 fraction | ||
97 | movew 4(%a0),%d0 | ||
98 | cmpl #0,%d0 |D0 has original exponent+fraction | ||
99 | bgts ACOSP1 | ||
100 | |||
101 | |--X = -1 | ||
102 | |Returns PI and inexact exception | ||
103 | fmovex PI,%fp0 | ||
104 | fmovel %d1,%FPCR | ||
105 | fadds #0x00800000,%fp0 |cause an inexact exception to be put | ||
106 | | ;into the 040 - will not trap until next | ||
107 | | ;fp inst. | ||
108 | bra t_frcinx | ||
109 | |||
110 | ACOSP1: | ||
111 | fmovel %d1,%FPCR | ||
112 | fmoves #0x00000000,%fp0 | ||
113 | rts |Facos ; of +1 is exact | ||
114 | |||
115 | |end | ||