1*         $NetBSD: satanh.sa,v 1.2 1994/10/26 07:49:33 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*         satanh.sa 3.3 12/19/90
35*
36*         The entry point satanh computes the inverse
37*         hyperbolic tangent of
38*         an input argument; satanhd does the same except for denormalized
39*         input.
40*
41*         Input: Double-extended number X in location pointed to
42*                   by address register a0.
43*
44*         Output: The value arctanh(X) returned in floating-point register Fp0.
45*
46*         Accuracy and Monotonicity: The returned result is within 3 ulps in
47*                   64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
48*                   result is subsequently rounded to double precision. The
49*                   result is provably monotonic in double precision.
50*
51*         Speed: The program satanh takes approximately 270 cycles.
52*
53*         Algorithm:
54*
55*         ATANH
56*         1. If |X| >= 1, go to 3.
57*
58*         2. (|X| < 1) Calculate atanh(X) by
59*                   sgn := sign(X)
60*                   y := |X|
61*                   z := 2y/(1-y)
62*                   atanh(X) := sgn * (1/2) * logp1(z)
63*                   Exit.
64*
65*         3. If |X| > 1, go to 5.
66*
67*         4. (|X| = 1) Generate infinity with an appropriate sign and
68*                   divide-by-zero by
69*                   sgn := sign(X)
70*                   atan(X) := sgn / (+0).
71*                   Exit.
72*
73*         5. (|X| > 1) Generate an invalid operation by 0 * infinity.
74*                   Exit.
75*
76
77satanh    IDNT      2,1 Motorola 040 Floating Point Software Package
78
79          section   8
80
81          xref      t_dz
82          xref      t_operr
83          xref      t_frcinx
84          xref      t_extdnrm
85          xref      slognp1
86
87          xdef      satanhd
88satanhd:
89*--ATANH(X) = X FOR DENORMALIZED X
90
91          bra                 t_extdnrm
92
93          xdef      satanh
94satanh:
95          move.l              (a0),d0
96          move.w              4(a0),d0
97          ANDI.L              #$7FFFFFFF,D0
98          CMPI.L              #$3FFF8000,D0
99          BGE.B               ATANHBIG
100
101*--THIS IS THE USUAL CASE, |X| < 1
102*--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
103
104          FABS.X              (a0),FP0  ...Y = |X|
105          FMOVE.X             FP0,FP1
106          FNEG.X              FP1                 ...-Y
107          FADD.X              FP0,FP0             ...2Y
108          FADD.S              #:3F800000,FP1      ...1-Y
109          FDIV.X              FP1,FP0             ...2Y/(1-Y)
110          move.l              (a0),d0
111          ANDI.L              #$80000000,D0
112          ORI.L               #$3F000000,D0       ...SIGN(X)*HALF
113          move.l              d0,-(sp)
114
115          fmovem.x  fp0,(a0)  ...overwrite input
116          move.l              d1,-(sp)
117          clr.l               d1
118          bsr                 slognp1             ...LOG1P(Z)
119          fmove.l             (sp)+,fpcr
120          FMUL.S              (sp)+,FP0
121          bra                 t_frcinx
122
123ATANHBIG:
124          FABS.X              (a0),FP0  ...|X|
125          FCMP.S              #:3F800000,FP0
126          fbgt                t_operr
127          bra                 t_dz
128
129          end
130