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1da177e4 LT |
1 | | |
2 | | slog2.sa 3.1 12/10/90 | |
3 | | | |
4 | | The entry point slog10 computes the base-10 | |
5 | | logarithm of an input argument X. | |
6 | | slog10d does the same except the input value is a | |
7 | | denormalized number. | |
8 | | sLog2 and sLog2d are the base-2 analogues. | |
9 | | | |
10 | | INPUT: Double-extended value in memory location pointed to | |
11 | | by address register a0. | |
12 | | | |
13 | | OUTPUT: log_10(X) or log_2(X) returned in floating-point | |
14 | | register fp0. | |
15 | | | |
16 | | ACCURACY and MONOTONICITY: The returned result is within 1.7 | |
17 | | ulps in 64 significant bit, i.e. within 0.5003 ulp | |
18 | | to 53 bits if the result is subsequently rounded | |
19 | | to double precision. The result is provably monotonic | |
20 | | in double precision. | |
21 | | | |
22 | | SPEED: Two timings are measured, both in the copy-back mode. | |
23 | | The first one is measured when the function is invoked | |
24 | | the first time (so the instructions and data are not | |
25 | | in cache), and the second one is measured when the | |
26 | | function is reinvoked at the same input argument. | |
27 | | | |
28 | | ALGORITHM and IMPLEMENTATION NOTES: | |
29 | | | |
30 | | slog10d: | |
31 | | | |
32 | | Step 0. If X < 0, create a NaN and raise the invalid operation | |
33 | | flag. Otherwise, save FPCR in D1; set FpCR to default. | |
34 | | Notes: Default means round-to-nearest mode, no floating-point | |
35 | | traps, and precision control = double extended. | |
36 | | | |
37 | | Step 1. Call slognd to obtain Y = log(X), the natural log of X. | |
38 | | Notes: Even if X is denormalized, log(X) is always normalized. | |
39 | | | |
40 | | Step 2. Compute log_10(X) = log(X) * (1/log(10)). | |
41 | | 2.1 Restore the user FPCR | |
42 | | 2.2 Return ans := Y * INV_L10. | |
43 | | | |
44 | | | |
45 | | slog10: | |
46 | | | |
47 | | Step 0. If X < 0, create a NaN and raise the invalid operation | |
48 | | flag. Otherwise, save FPCR in D1; set FpCR to default. | |
49 | | Notes: Default means round-to-nearest mode, no floating-point | |
50 | | traps, and precision control = double extended. | |
51 | | | |
52 | | Step 1. Call sLogN to obtain Y = log(X), the natural log of X. | |
53 | | | |
54 | | Step 2. Compute log_10(X) = log(X) * (1/log(10)). | |
55 | | 2.1 Restore the user FPCR | |
56 | | 2.2 Return ans := Y * INV_L10. | |
57 | | | |
58 | | | |
59 | | sLog2d: | |
60 | | | |
61 | | Step 0. If X < 0, create a NaN and raise the invalid operation | |
62 | | flag. Otherwise, save FPCR in D1; set FpCR to default. | |
63 | | Notes: Default means round-to-nearest mode, no floating-point | |
64 | | traps, and precision control = double extended. | |
65 | | | |
66 | | Step 1. Call slognd to obtain Y = log(X), the natural log of X. | |
67 | | Notes: Even if X is denormalized, log(X) is always normalized. | |
68 | | | |
69 | | Step 2. Compute log_10(X) = log(X) * (1/log(2)). | |
70 | | 2.1 Restore the user FPCR | |
71 | | 2.2 Return ans := Y * INV_L2. | |
72 | | | |
73 | | | |
74 | | sLog2: | |
75 | | | |
76 | | Step 0. If X < 0, create a NaN and raise the invalid operation | |
77 | | flag. Otherwise, save FPCR in D1; set FpCR to default. | |
78 | | Notes: Default means round-to-nearest mode, no floating-point | |
79 | | traps, and precision control = double extended. | |
80 | | | |
81 | | Step 1. If X is not an integer power of two, i.e., X != 2^k, | |
82 | | go to Step 3. | |
83 | | | |
84 | | Step 2. Return k. | |
85 | | 2.1 Get integer k, X = 2^k. | |
86 | | 2.2 Restore the user FPCR. | |
87 | | 2.3 Return ans := convert-to-double-extended(k). | |
88 | | | |
89 | | Step 3. Call sLogN to obtain Y = log(X), the natural log of X. | |
90 | | | |
91 | | Step 4. Compute log_2(X) = log(X) * (1/log(2)). | |
92 | | 4.1 Restore the user FPCR | |
93 | | 4.2 Return ans := Y * INV_L2. | |
94 | | | |
95 | ||
96 | | Copyright (C) Motorola, Inc. 1990 | |
97 | | All Rights Reserved | |
98 | | | |
99 | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | |
100 | | The copyright notice above does not evidence any | |
101 | | actual or intended publication of such source code. | |
102 | ||
103 | |SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package | |
104 | ||
105 | |section 8 | |
106 | ||
107 | |xref t_frcinx | |
108 | |xref t_operr | |
109 | |xref slogn | |
110 | |xref slognd | |
111 | ||
112 | INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 | |
113 | ||
114 | INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 | |
115 | ||
116 | .global slog10d | |
117 | slog10d: | |
118 | |--entry point for Log10(X), X is denormalized | |
119 | movel (%a0),%d0 | |
120 | blt invalid | |
121 | movel %d1,-(%sp) | |
122 | clrl %d1 | |
123 | bsr slognd | ...log(X), X denorm. | |
124 | fmovel (%sp)+,%fpcr | |
125 | fmulx INV_L10,%fp0 | |
126 | bra t_frcinx | |
127 | ||
128 | .global slog10 | |
129 | slog10: | |
130 | |--entry point for Log10(X), X is normalized | |
131 | ||
132 | movel (%a0),%d0 | |
133 | blt invalid | |
134 | movel %d1,-(%sp) | |
135 | clrl %d1 | |
136 | bsr slogn | ...log(X), X normal. | |
137 | fmovel (%sp)+,%fpcr | |
138 | fmulx INV_L10,%fp0 | |
139 | bra t_frcinx | |
140 | ||
141 | ||
142 | .global slog2d | |
143 | slog2d: | |
144 | |--entry point for Log2(X), X is denormalized | |
145 | ||
146 | movel (%a0),%d0 | |
147 | blt invalid | |
148 | movel %d1,-(%sp) | |
149 | clrl %d1 | |
150 | bsr slognd | ...log(X), X denorm. | |
151 | fmovel (%sp)+,%fpcr | |
152 | fmulx INV_L2,%fp0 | |
153 | bra t_frcinx | |
154 | ||
155 | .global slog2 | |
156 | slog2: | |
157 | |--entry point for Log2(X), X is normalized | |
158 | movel (%a0),%d0 | |
159 | blt invalid | |
160 | ||
161 | movel 8(%a0),%d0 | |
162 | bnes continue | ...X is not 2^k | |
163 | ||
164 | movel 4(%a0),%d0 | |
165 | andl #0x7FFFFFFF,%d0 | |
166 | tstl %d0 | |
167 | bnes continue | |
168 | ||
169 | |--X = 2^k. | |
170 | movew (%a0),%d0 | |
171 | andl #0x00007FFF,%d0 | |
172 | subl #0x3FFF,%d0 | |
173 | fmovel %d1,%fpcr | |
174 | fmovel %d0,%fp0 | |
175 | bra t_frcinx | |
176 | ||
177 | continue: | |
178 | movel %d1,-(%sp) | |
179 | clrl %d1 | |
180 | bsr slogn | ...log(X), X normal. | |
181 | fmovel (%sp)+,%fpcr | |
182 | fmulx INV_L2,%fp0 | |
183 | bra t_frcinx | |
184 | ||
185 | invalid: | |
186 | bra t_operr | |
187 | ||
188 | |end |