Commit | Line | Data |
---|---|---|
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 | | | |
e00d82d0 MW |
99 | | For details on the license for this file, please see the |
100 | | file, README, in this same directory. | |
1da177e4 LT |
101 | |
102 | |SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package | |
103 | ||
104 | |section 8 | |
105 | ||
106 | |xref t_frcinx | |
107 | |xref t_operr | |
108 | |xref slogn | |
109 | |xref slognd | |
110 | ||
111 | INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 | |
112 | ||
113 | INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 | |
114 | ||
115 | .global slog10d | |
116 | slog10d: | |
117 | |--entry point for Log10(X), X is denormalized | |
118 | movel (%a0),%d0 | |
119 | blt invalid | |
120 | movel %d1,-(%sp) | |
121 | clrl %d1 | |
122 | bsr slognd | ...log(X), X denorm. | |
123 | fmovel (%sp)+,%fpcr | |
124 | fmulx INV_L10,%fp0 | |
125 | bra t_frcinx | |
126 | ||
127 | .global slog10 | |
128 | slog10: | |
129 | |--entry point for Log10(X), X is normalized | |
130 | ||
131 | movel (%a0),%d0 | |
132 | blt invalid | |
133 | movel %d1,-(%sp) | |
134 | clrl %d1 | |
135 | bsr slogn | ...log(X), X normal. | |
136 | fmovel (%sp)+,%fpcr | |
137 | fmulx INV_L10,%fp0 | |
138 | bra t_frcinx | |
139 | ||
140 | ||
141 | .global slog2d | |
142 | slog2d: | |
143 | |--entry point for Log2(X), X is denormalized | |
144 | ||
145 | movel (%a0),%d0 | |
146 | blt invalid | |
147 | movel %d1,-(%sp) | |
148 | clrl %d1 | |
149 | bsr slognd | ...log(X), X denorm. | |
150 | fmovel (%sp)+,%fpcr | |
151 | fmulx INV_L2,%fp0 | |
152 | bra t_frcinx | |
153 | ||
154 | .global slog2 | |
155 | slog2: | |
156 | |--entry point for Log2(X), X is normalized | |
157 | movel (%a0),%d0 | |
158 | blt invalid | |
159 | ||
160 | movel 8(%a0),%d0 | |
161 | bnes continue | ...X is not 2^k | |
162 | ||
163 | movel 4(%a0),%d0 | |
164 | andl #0x7FFFFFFF,%d0 | |
165 | tstl %d0 | |
166 | bnes continue | |
167 | ||
168 | |--X = 2^k. | |
169 | movew (%a0),%d0 | |
170 | andl #0x00007FFF,%d0 | |
171 | subl #0x3FFF,%d0 | |
172 | fmovel %d1,%fpcr | |
173 | fmovel %d0,%fp0 | |
174 | bra t_frcinx | |
175 | ||
176 | continue: | |
177 | movel %d1,-(%sp) | |
178 | clrl %d1 | |
179 | bsr slogn | ...log(X), X normal. | |
180 | fmovel (%sp)+,%fpcr | |
181 | fmulx INV_L2,%fp0 | |
182 | bra t_frcinx | |
183 | ||
184 | invalid: | |
185 | bra t_operr | |
186 | ||
187 | |end |