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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41| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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
49PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
50PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
51
52 |xref t_operr
53 |xref t_frcinx
54 |xref satan
55
56 .global sacosd
57sacosd:
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
64sacos:
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
90ACOSBIG:
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
110ACOSP1:
111 fmovel %d1,%FPCR
112 fmoves #0x00000000,%fp0
113 rts |Facos ; of +1 is exact
114
115 |end