1*         $NetBSD: sacos.sa,v 1.3 1994/10/26 07:49:27 cgd Exp $
2
3*         MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
4*         M68000 Hi-Performance Microprocessor Division
5*         M68040 Software Package
6*
7*         M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
8*         All rights reserved.
9*
10*         THE SOFTWARE is provided on an "AS IS" basis and without warranty.
11*         To the maximum extent permitted by applicable law,
12*         MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
13*         INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
14*         PARTICULAR PURPOSE and any warranty against infringement with
15*         regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
16*         and any accompanying written materials.
17*
18*         To the maximum extent permitted by applicable law,
19*         IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
20*         (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
21*         PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
22*         OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
23*         SOFTWARE.  Motorola assumes no responsibility for the maintenance
24*         and support of the SOFTWARE.
25*
26*         You are hereby granted a copyright license to use, modify, and
27*         distribute the SOFTWARE so long as this entire notice is retained
28*         without alteration in any modified and/or redistributed versions,
29*         and that such modified versions are clearly identified as such.
30*         No licenses are granted by implication, estoppel or otherwise
31*         under any patents or trademarks of Motorola, Inc.
32
33*
34*         sacos.sa 3.3 12/19/90
35*
36*         Description: The entry point sAcos computes the inverse cosine of
37*                   an input argument; sAcosd does the same except for denormalized
38*                   input.
39*
40*         Input: Double-extended number X in location pointed to
41*                   by address register a0.
42*
43*         Output: The value arccos(X) returned in floating-point register Fp0.
44*
45*         Accuracy and Monotonicity: The returned result is within 3 ulps in
46*                   64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
47*                   result is subsequently rounded to double precision. The
48*                   result is provably monotonic in double precision.
49*
50*         Speed: The program sCOS takes approximately 310 cycles.
51*
52*         Algorithm:
53*
54*         ACOS
55*         1. If |X| >= 1, go to 3.
56*
57*         2. (|X| < 1) Calculate acos(X) by
58*                   z := (1-X) / (1+X)
59*                   acos(X) = 2 * atan( sqrt(z) ).
60*                   Exit.
61*
62*         3. If |X| > 1, go to 5.
63*
64*         4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
65*
66*         5. (|X| > 1) Generate an invalid operation by 0 * infinity.
67*                   Exit.
68*
69
70SACOS     IDNT      2,1 Motorola 040 Floating Point Software Package
71
72          section   8
73
74PI        DC.L $40000000,$C90FDAA2,$2168C235,$00000000
75PIBY2     DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
76
77          xref      t_operr
78          xref      t_frcinx
79          xref      satan
80
81          xdef      sacosd
82sacosd:
83*--ACOS(X) = PI/2 FOR DENORMALIZED X
84          fmove.l             d1,fpcr             ...load user's rounding mode/precision
85          FMOVE.X             PIBY2,FP0
86          bra                 t_frcinx
87
88          xdef      sacos
89sacos:
90          FMOVE.X             (a0),FP0  ...LOAD INPUT
91
92          move.l              (a0),d0             ...pack exponent with upper 16 fraction
93          move.w              4(a0),d0
94          ANDI.L              #$7FFFFFFF,D0
95          CMPI.L              #$3FFF8000,D0
96          BGE.B               ACOSBIG
97
98*--THIS IS THE USUAL CASE, |X| < 1
99*--ACOS(X) = 2 * ATAN(        SQRT( (1-X)/(1+X) ) )
100
101          FMOVE.S             #:3F800000,FP1
102          FADD.X              FP0,FP1             ...1+X
103          FNEG.X              FP0                 ... -X
104          FADD.S              #:3F800000,FP0      ...1-X
105          FDIV.X              FP1,FP0             ...(1-X)/(1+X)
106          FSQRT.X             FP0                 ...SQRT((1-X)/(1+X))
107          fmovem.x  fp0,(a0)  ...overwrite input
108          move.l              d1,-(sp)  ;save original users fpcr
109          clr.l               d1
110          bsr                 satan               ...ATAN(SQRT([1-X]/[1+X]))
111          fMOVE.L             (sp)+,fpcr          ;restore users exceptions
112          FADD.X              FP0,FP0             ...2 * ATAN( STUFF )
113          bra                 t_frcinx
114
115ACOSBIG:
116          FABS.X              FP0
117          FCMP.S              #:3F800000,FP0
118          fbgt                t_operr             ;cause an operr exception
119
120*--|X| = 1, ACOS(X) = 0 OR PI
121          move.l              (a0),d0             ...pack exponent with upper 16 fraction
122          move.w              4(a0),d0
123          TST.L               D0                  ;D0 has original exponent+fraction
124          BGT.B               ACOSP1
125
126*--X = -1
127*Returns PI and inexact exception
128          FMOVE.X             PI,FP0
129          FMOVE.L             d1,FPCR
130          FADD.S              #:00800000,FP0      ;cause an inexact exception to be put
131*                                                 ;into the 040 - will not trap until next
132*                                                 ;fp inst.
133          bra                 t_frcinx
134
135ACOSP1:
136          FMOVE.L             d1,FPCR
137          FMOVE.S             #:00000000,FP0
138          rts                                     ;Facos of +1 is exact
139
140          end
141