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|
|       sacos.sa 3.3 12/19/90
|
|       Description: The entry point sAcos computes the inverse cosine of
|               an input argument; sAcosd does the same except for denormalized
|               input.
|
|       Input: Double-extended number X in location pointed to
|               by address register a0.
|
|       Output: The value arccos(X) returned in floating-point register Fp0.
|
|       Accuracy and Monotonicity: The returned result is within 3 ulps in
|               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|               result is subsequently rounded to double precision. The
|               result is provably monotonic in double precision.
|
|       Speed: The program sCOS takes approximately 310 cycles.
|
|       Algorithm:
|
|       ACOS
|       1. If |X| >= 1, go to 3.
|
|       2. (|X| < 1) Calculate acos(X) by
|               z := (1-X) / (1+X)
|               acos(X) = 2 * atan( sqrt(z) ).
|               Exit.
|
|       3. If |X| > 1, go to 5.
|
|       4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
|
|       5. (|X| > 1) Generate an invalid operation by 0 * infinity.
|               Exit.
|
 
|               Copyright (C) Motorola, Inc. 1990
|                       All Rights Reserved
|
|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|       The copyright notice above does not evidence any
|       actual or intended publication of such source code.
 
|SACOS  idnt    2,1 | Motorola 040 Floating Point Software Package
 
        |section        8
 
PI:     .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
PIBY2:  .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
 
        |xref   t_operr
        |xref   t_frcinx
        |xref   satan
 
        .global sacosd
sacosd:
|--ACOS(X) = PI/2 FOR DENORMALIZED X
        fmovel          %d1,%fpcr               | ...load user's rounding mode/precision
        fmovex          PIBY2,%fp0
        bra             t_frcinx
 
        .global sacos
sacos:
        fmovex          (%a0),%fp0      | ...LOAD INPUT
 
        movel           (%a0),%d0               | ...pack exponent with upper 16 fraction
        movew           4(%a0),%d0
        andil           #0x7FFFFFFF,%d0
        cmpil           #0x3FFF8000,%d0
        bges            ACOSBIG
 
|--THIS IS THE USUAL CASE, |X| < 1
|--ACOS(X) = 2 * ATAN(  SQRT( (1-X)/(1+X) )     )
 
        fmoves          #0x3F800000,%fp1
        faddx           %fp0,%fp1               | ...1+X
        fnegx           %fp0            | ... -X
        fadds           #0x3F800000,%fp0        | ...1-X
        fdivx           %fp1,%fp0               | ...(1-X)/(1+X)
        fsqrtx          %fp0            | ...SQRT((1-X)/(1+X))
        fmovemx %fp0-%fp0,(%a0) | ...overwrite input
        movel           %d1,-(%sp)      |save original users fpcr
        clrl            %d1
        bsr             satan           | ...ATAN(SQRT([1-X]/[1+X]))
        fmovel          (%sp)+,%fpcr    |restore users exceptions
        faddx           %fp0,%fp0               | ...2 * ATAN( STUFF )
        bra             t_frcinx
 
ACOSBIG:
        fabsx           %fp0
        fcmps           #0x3F800000,%fp0
        fbgt            t_operr         |cause an operr exception
 
|--|X| = 1, ACOS(X) = 0 OR PI
        movel           (%a0),%d0               | ...pack exponent with upper 16 fraction
        movew           4(%a0),%d0
        cmpl            #0,%d0          |D0 has original exponent+fraction
        bgts            ACOSP1
 
|--X = -1
|Returns PI and inexact exception
        fmovex          PI,%fp0
        fmovel          %d1,%FPCR
        fadds           #0x00800000,%fp0        |cause an inexact exception to be put
|                                       ;into the 040 - will not trap until next
|                                       ;fp inst.
        bra             t_frcinx
 
ACOSP1:
        fmovel          %d1,%FPCR
        fmoves          #0x00000000,%fp0
        rts                             |Facos ; of +1 is exact
 
        |end

Line No.	Rev	Author	Line
1	1623	jcastillo	`\|`
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`

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[/] [or1k/] [trunk/] [rc203soc/] [sw/] [uClinux/] [arch/] [m68k/] [fpsp040/] [sacos.S] - Blame information for rev 1623