[PATCH] Add wording to m68k .S files to help clarify license info
[linux-3.10.git] / arch / m68k / fpsp040 / stanh.S
1 |
2 |       stanh.sa 3.1 12/10/90
3 |
4 |       The entry point sTanh computes the hyperbolic tangent of
5 |       an input argument; sTanhd 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 tanh(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 stanh takes approximately 270 cycles.
19 |
20 |       Algorithm:
21 |
22 |       TANH
23 |       1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
24 |
25 |       2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
26 |               sgn := sign(X), y := 2|X|, z := expm1(Y), and
27 |               tanh(X) = sgn*( z/(2+z) ).
28 |               Exit.
29 |
30 |       3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
31 |               go to 7.
32 |
33 |       4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
34 |
35 |       5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
36 |               sgn := sign(X), y := 2|X|, z := exp(Y),
37 |               tanh(X) = sgn - [ sgn*2/(1+z) ].
38 |               Exit.
39 |
40 |       6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
41 |               calculate Tanh(X) by
42 |               sgn := sign(X), Tiny := 2**(-126),
43 |               tanh(X) := sgn - sgn*Tiny.
44 |               Exit.
45 |
46 |       7. (|X| < 2**(-40)). Tanh(X) = X.       Exit.
47 |
48
49 |               Copyright (C) Motorola, Inc. 1990
50 |                       All Rights Reserved
51 |
52 |       For details on the license for this file, please see the
53 |       file, README, in this same directory.
54
55 |STANH  idnt    2,1 | Motorola 040 Floating Point Software Package
56
57         |section        8
58
59 #include "fpsp.h"
60
61         .set    X,FP_SCR5
62         .set    XDCARE,X+2
63         .set    XFRAC,X+4
64
65         .set    SGN,L_SCR3
66
67         .set    V,FP_SCR6
68
69 BOUNDS1:        .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
70
71         |xref   t_frcinx
72         |xref   t_extdnrm
73         |xref   setox
74         |xref   setoxm1
75
76         .global stanhd
77 stanhd:
78 |--TANH(X) = X FOR DENORMALIZED X
79
80         bra             t_extdnrm
81
82         .global stanh
83 stanh:
84         fmovex          (%a0),%fp0      | ...LOAD INPUT
85
86         fmovex          %fp0,X(%a6)
87         movel           (%a0),%d0
88         movew           4(%a0),%d0
89         movel           %d0,X(%a6)
90         andl            #0x7FFFFFFF,%d0
91         cmp2l           BOUNDS1(%pc),%d0        | ...2**(-40) < |X| < (5/2)LOG2 ?
92         bcss            TANHBORS
93
94 |--THIS IS THE USUAL CASE
95 |--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
96
97         movel           X(%a6),%d0
98         movel           %d0,SGN(%a6)
99         andl            #0x7FFF0000,%d0
100         addl            #0x00010000,%d0 | ...EXPONENT OF 2|X|
101         movel           %d0,X(%a6)
102         andl            #0x80000000,SGN(%a6)
103         fmovex          X(%a6),%fp0             | ...FP0 IS Y = 2|X|
104
105         movel           %d1,-(%a7)
106         clrl            %d1
107         fmovemx %fp0-%fp0,(%a0)
108         bsr             setoxm1         | ...FP0 IS Z = EXPM1(Y)
109         movel           (%a7)+,%d1
110
111         fmovex          %fp0,%fp1
112         fadds           #0x40000000,%fp1        | ...Z+2
113         movel           SGN(%a6),%d0
114         fmovex          %fp1,V(%a6)
115         eorl            %d0,V(%a6)
116
117         fmovel          %d1,%FPCR               |restore users exceptions
118         fdivx           V(%a6),%fp0
119         bra             t_frcinx
120
121 TANHBORS:
122         cmpl            #0x3FFF8000,%d0
123         blt             TANHSM
124
125         cmpl            #0x40048AA1,%d0
126         bgt             TANHHUGE
127
128 |-- (5/2) LOG2 < |X| < 50 LOG2,
129 |--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
130 |--TANH(X) = SGN -      SGN*2/[EXP(Y)+1].
131
132         movel           X(%a6),%d0
133         movel           %d0,SGN(%a6)
134         andl            #0x7FFF0000,%d0
135         addl            #0x00010000,%d0 | ...EXPO OF 2|X|
136         movel           %d0,X(%a6)              | ...Y = 2|X|
137         andl            #0x80000000,SGN(%a6)
138         movel           SGN(%a6),%d0
139         fmovex          X(%a6),%fp0             | ...Y = 2|X|
140
141         movel           %d1,-(%a7)
142         clrl            %d1
143         fmovemx %fp0-%fp0,(%a0)
144         bsr             setox           | ...FP0 IS EXP(Y)
145         movel           (%a7)+,%d1
146         movel           SGN(%a6),%d0
147         fadds           #0x3F800000,%fp0        | ...EXP(Y)+1
148
149         eorl            #0xC0000000,%d0 | ...-SIGN(X)*2
150         fmoves          %d0,%fp1                | ...-SIGN(X)*2 IN SGL FMT
151         fdivx           %fp0,%fp1               | ...-SIGN(X)2 / [EXP(Y)+1 ]
152
153         movel           SGN(%a6),%d0
154         orl             #0x3F800000,%d0 | ...SGN
155         fmoves          %d0,%fp0                | ...SGN IN SGL FMT
156
157         fmovel          %d1,%FPCR               |restore users exceptions
158         faddx           %fp1,%fp0
159
160         bra             t_frcinx
161
162 TANHSM:
163         movew           #0x0000,XDCARE(%a6)
164
165         fmovel          %d1,%FPCR               |restore users exceptions
166         fmovex          X(%a6),%fp0             |last inst - possible exception set
167
168         bra             t_frcinx
169
170 TANHHUGE:
171 |---RETURN SGN(X) - SGN(X)EPS
172         movel           X(%a6),%d0
173         andl            #0x80000000,%d0
174         orl             #0x3F800000,%d0
175         fmoves          %d0,%fp0
176         andl            #0x80000000,%d0
177         eorl            #0x80800000,%d0 | ...-SIGN(X)*EPS
178
179         fmovel          %d1,%FPCR               |restore users exceptions
180         fadds           %d0,%fp0
181
182         bra             t_frcinx
183
184         |end