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Linus Torvalds1da177e2005-04-16 15:20:36 -07001|
2| satanh.sa 3.3 12/19/90
3|
4| The entry point satanh computes the inverse
5| hyperbolic tangent of
6| an input argument; satanhd does the same except for denormalized
7| input.
8|
9| Input: Double-extended number X in location pointed to
10| by address register a0.
11|
12| Output: The value arctanh(X) returned in floating-point register Fp0.
13|
14| Accuracy and Monotonicity: The returned result is within 3 ulps in
15| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
16| result is subsequently rounded to double precision. The
17| result is provably monotonic in double precision.
18|
19| Speed: The program satanh takes approximately 270 cycles.
20|
21| Algorithm:
22|
23| ATANH
24| 1. If |X| >= 1, go to 3.
25|
26| 2. (|X| < 1) Calculate atanh(X) by
27| sgn := sign(X)
28| y := |X|
29| z := 2y/(1-y)
30| atanh(X) := sgn * (1/2) * logp1(z)
31| Exit.
32|
33| 3. If |X| > 1, go to 5.
34|
35| 4. (|X| = 1) Generate infinity with an appropriate sign and
36| divide-by-zero by
37| sgn := sign(X)
38| atan(X) := sgn / (+0).
39| Exit.
40|
41| 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
42| Exit.
43|
44
45| Copyright (C) Motorola, Inc. 1990
46| All Rights Reserved
47|
48| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
49| The copyright notice above does not evidence any
50| actual or intended publication of such source code.
51
52|satanh idnt 2,1 | Motorola 040 Floating Point Software Package
53
54 |section 8
55
56 |xref t_dz
57 |xref t_operr
58 |xref t_frcinx
59 |xref t_extdnrm
60 |xref slognp1
61
62 .global satanhd
63satanhd:
64|--ATANH(X) = X FOR DENORMALIZED X
65
66 bra t_extdnrm
67
68 .global satanh
69satanh:
70 movel (%a0),%d0
71 movew 4(%a0),%d0
72 andil #0x7FFFFFFF,%d0
73 cmpil #0x3FFF8000,%d0
74 bges ATANHBIG
75
76|--THIS IS THE USUAL CASE, |X| < 1
77|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
78
79 fabsx (%a0),%fp0 | ...Y = |X|
80 fmovex %fp0,%fp1
81 fnegx %fp1 | ...-Y
82 faddx %fp0,%fp0 | ...2Y
83 fadds #0x3F800000,%fp1 | ...1-Y
84 fdivx %fp1,%fp0 | ...2Y/(1-Y)
85 movel (%a0),%d0
86 andil #0x80000000,%d0
87 oril #0x3F000000,%d0 | ...SIGN(X)*HALF
88 movel %d0,-(%sp)
89
90 fmovemx %fp0-%fp0,(%a0) | ...overwrite input
91 movel %d1,-(%sp)
92 clrl %d1
93 bsr slognp1 | ...LOG1P(Z)
94 fmovel (%sp)+,%fpcr
95 fmuls (%sp)+,%fp0
96 bra t_frcinx
97
98ATANHBIG:
99 fabsx (%a0),%fp0 | ...|X|
100 fcmps #0x3F800000,%fp0
101 fbgt t_operr
102 bra t_dz
103
104 |end