sasin.sa revision 1.1 1 1.1 mycroft * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
2 1.1 mycroft * M68000 Hi-Performance Microprocessor Division
3 1.1 mycroft * M68040 Software Package
4 1.1 mycroft *
5 1.1 mycroft * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
6 1.1 mycroft * All rights reserved.
7 1.1 mycroft *
8 1.1 mycroft * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
9 1.1 mycroft * To the maximum extent permitted by applicable law,
10 1.1 mycroft * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
11 1.1 mycroft * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
12 1.1 mycroft * PARTICULAR PURPOSE and any warranty against infringement with
13 1.1 mycroft * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
14 1.1 mycroft * and any accompanying written materials.
15 1.1 mycroft *
16 1.1 mycroft * To the maximum extent permitted by applicable law,
17 1.1 mycroft * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
18 1.1 mycroft * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
19 1.1 mycroft * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
20 1.1 mycroft * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
21 1.1 mycroft * SOFTWARE. Motorola assumes no responsibility for the maintenance
22 1.1 mycroft * and support of the SOFTWARE.
23 1.1 mycroft *
24 1.1 mycroft * You are hereby granted a copyright license to use, modify, and
25 1.1 mycroft * distribute the SOFTWARE so long as this entire notice is retained
26 1.1 mycroft * without alteration in any modified and/or redistributed versions,
27 1.1 mycroft * and that such modified versions are clearly identified as such.
28 1.1 mycroft * No licenses are granted by implication, estoppel or otherwise
29 1.1 mycroft * under any patents or trademarks of Motorola, Inc.
30 1.1 mycroft
31 1.1 mycroft *
32 1.1 mycroft * sasin.sa 3.3 12/19/90
33 1.1 mycroft *
34 1.1 mycroft * Description: The entry point sAsin computes the inverse sine of
35 1.1 mycroft * an input argument; sAsind does the same except for denormalized
36 1.1 mycroft * input.
37 1.1 mycroft *
38 1.1 mycroft * Input: Double-extended number X in location pointed to
39 1.1 mycroft * by address register a0.
40 1.1 mycroft *
41 1.1 mycroft * Output: The value arcsin(X) returned in floating-point register Fp0.
42 1.1 mycroft *
43 1.1 mycroft * Accuracy and Monotonicity: The returned result is within 3 ulps in
44 1.1 mycroft * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
45 1.1 mycroft * result is subsequently rounded to double precision. The
46 1.1 mycroft * result is provably monotonic in double precision.
47 1.1 mycroft *
48 1.1 mycroft * Speed: The program sASIN takes approximately 310 cycles.
49 1.1 mycroft *
50 1.1 mycroft * Algorithm:
51 1.1 mycroft *
52 1.1 mycroft * ASIN
53 1.1 mycroft * 1. If |X| >= 1, go to 3.
54 1.1 mycroft *
55 1.1 mycroft * 2. (|X| < 1) Calculate asin(X) by
56 1.1 mycroft * z := sqrt( [1-X][1+X] )
57 1.1 mycroft * asin(X) = atan( x / z ).
58 1.1 mycroft * Exit.
59 1.1 mycroft *
60 1.1 mycroft * 3. If |X| > 1, go to 5.
61 1.1 mycroft *
62 1.1 mycroft * 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
63 1.1 mycroft *
64 1.1 mycroft * 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
65 1.1 mycroft * Exit.
66 1.1 mycroft *
67 1.1 mycroft
68 1.1 mycroft SASIN IDNT 2,1 Motorola 040 Floating Point Software Package
69 1.1 mycroft
70 1.1 mycroft section 8
71 1.1 mycroft
72 1.1 mycroft PIBY2 DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
73 1.1 mycroft
74 1.1 mycroft xref t_operr
75 1.1 mycroft xref t_frcinx
76 1.1 mycroft xref t_extdnrm
77 1.1 mycroft xref satan
78 1.1 mycroft
79 1.1 mycroft xdef sasind
80 1.1 mycroft sasind:
81 1.1 mycroft *--ASIN(X) = X FOR DENORMALIZED X
82 1.1 mycroft
83 1.1 mycroft bra t_extdnrm
84 1.1 mycroft
85 1.1 mycroft xdef sasin
86 1.1 mycroft sasin:
87 1.1 mycroft FMOVE.X (a0),FP0 ...LOAD INPUT
88 1.1 mycroft
89 1.1 mycroft move.l (a0),d0
90 1.1 mycroft move.w 4(a0),d0
91 1.1 mycroft ANDI.L #$7FFFFFFF,D0
92 1.1 mycroft CMPI.L #$3FFF8000,D0
93 1.1 mycroft BGE.B asinbig
94 1.1 mycroft
95 1.1 mycroft *--THIS IS THE USUAL CASE, |X| < 1
96 1.1 mycroft *--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
97 1.1 mycroft
98 1.1 mycroft FMOVE.S #:3F800000,FP1
99 1.1 mycroft FSUB.X FP0,FP1 ...1-X
100 1.1 mycroft fmovem.x fp2,-(a7)
101 1.1 mycroft FMOVE.S #:3F800000,FP2
102 1.1 mycroft FADD.X FP0,FP2 ...1+X
103 1.1 mycroft FMUL.X FP2,FP1 ...(1+X)(1-X)
104 1.1 mycroft fmovem.x (a7)+,fp2
105 1.1 mycroft FSQRT.X FP1 ...SQRT([1-X][1+X])
106 1.1 mycroft FDIV.X FP1,FP0 ...X/SQRT([1-X][1+X])
107 1.1 mycroft fmovem.x fp0,(a0)
108 1.1 mycroft bsr satan
109 1.1 mycroft bra t_frcinx
110 1.1 mycroft
111 1.1 mycroft asinbig:
112 1.1 mycroft FABS.X FP0 ...|X|
113 1.1 mycroft FCMP.S #:3F800000,FP0
114 1.1 mycroft fbgt t_operr ;cause an operr exception
115 1.1 mycroft
116 1.1 mycroft *--|X| = 1, ASIN(X) = +- PI/2.
117 1.1 mycroft
118 1.1 mycroft FMOVE.X PIBY2,FP0
119 1.1 mycroft move.l (a0),d0
120 1.1 mycroft ANDI.L #$80000000,D0 ...SIGN BIT OF X
121 1.1 mycroft ORI.L #$3F800000,D0 ...+-1 IN SGL FORMAT
122 1.1 mycroft MOVE.L D0,-(sp) ...push SIGN(X) IN SGL-FMT
123 1.1 mycroft FMOVE.L d1,FPCR
124 1.1 mycroft FMUL.S (sp)+,FP0
125 1.1 mycroft bra t_frcinx
126 1.1 mycroft
127 1.1 mycroft end
128