1 | 1 |
2 | slog2.sa 3.1 12/10/90 2 | slog2.sa 3.1 12/10/90
3 | 3 |
4 | The entry point slog10 computes the ba !! 4 | The entry point slog10 computes the base-10
5 | logarithm of an input argument X. 5 | logarithm of an input argument X.
6 | slog10d does the same except the input !! 6 | slog10d does the same except the input value is a
7 | denormalized number. !! 7 | denormalized number.
8 | sLog2 and sLog2d are the base-2 analog 8 | sLog2 and sLog2d are the base-2 analogues.
9 | 9 |
10 | INPUT: Double-extended value in memor !! 10 | INPUT: Double-extended value in memory location pointed to
11 | by address register a0. 11 | by address register a0.
12 | 12 |
13 | OUTPUT: log_10(X) or log_2(X) returned !! 13 | OUTPUT: log_10(X) or log_2(X) returned in floating-point
14 | register fp0. 14 | register fp0.
15 | 15 |
16 | ACCURACY and MONOTONICITY: The returne !! 16 | ACCURACY and MONOTONICITY: The returned result is within 1.7
17 | ulps in 64 significant bit, i. !! 17 | ulps in 64 significant bit, i.e. within 0.5003 ulp
18 | to 53 bits if the result is su !! 18 | to 53 bits if the result is subsequently rounded
19 | to double precision. The resul !! 19 | to double precision. The result is provably monotonic
20 | in double precision. 20 | in double precision.
21 | 21 |
22 | SPEED: Two timings are measured, both !! 22 | SPEED: Two timings are measured, both in the copy-back mode.
23 | The first one is measured when !! 23 | The first one is measured when the function is invoked
24 | the first time (so the instruc !! 24 | the first time (so the instructions and data are not
25 | in cache), and the second one !! 25 | in cache), and the second one is measured when the
26 | function is reinvoked at the s 26 | function is reinvoked at the same input argument.
27 | 27 |
28 | ALGORITHM and IMPLEMENTATION NOTES: 28 | ALGORITHM and IMPLEMENTATION NOTES:
29 | 29 |
30 | slog10d: 30 | slog10d:
31 | 31 |
32 | Step 0. If X < 0, create a NaN and r 32 | Step 0. If X < 0, create a NaN and raise the invalid operation
33 | flag. Otherwise, save FPCR i 33 | flag. Otherwise, save FPCR in D1; set FpCR to default.
34 | Notes: Default means round-to-neare 34 | Notes: Default means round-to-nearest mode, no floating-point
35 | traps, and precision control 35 | traps, and precision control = double extended.
36 | 36 |
37 | Step 1. Call slognd to obtain Y = lo 37 | Step 1. Call slognd to obtain Y = log(X), the natural log of X.
38 | Notes: Even if X is denormalized, l 38 | Notes: Even if X is denormalized, log(X) is always normalized.
39 | 39 |
40 | Step 2. Compute log_10(X) = log(X) * 40 | Step 2. Compute log_10(X) = log(X) * (1/log(10)).
41 | 2.1 Restore the user FPCR 41 | 2.1 Restore the user FPCR
42 | 2.2 Return ans := Y * INV_L10. 42 | 2.2 Return ans := Y * INV_L10.
43 | 43 |
44 | 44 |
45 | slog10: !! 45 | slog10:
46 | 46 |
47 | Step 0. If X < 0, create a NaN and r 47 | Step 0. If X < 0, create a NaN and raise the invalid operation
48 | flag. Otherwise, save FPCR i 48 | flag. Otherwise, save FPCR in D1; set FpCR to default.
49 | Notes: Default means round-to-neare 49 | Notes: Default means round-to-nearest mode, no floating-point
50 | traps, and precision control 50 | traps, and precision control = double extended.
51 | 51 |
52 | Step 1. Call sLogN to obtain Y = log 52 | Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
53 | 53 |
54 | Step 2. Compute log_10(X) = log(X) * 54 | Step 2. Compute log_10(X) = log(X) * (1/log(10)).
55 | 2.1 Restore the user FPCR 55 | 2.1 Restore the user FPCR
56 | 2.2 Return ans := Y * INV_L10. 56 | 2.2 Return ans := Y * INV_L10.
57 | 57 |
58 | 58 |
59 | sLog2d: 59 | sLog2d:
60 | 60 |
61 | Step 0. If X < 0, create a NaN and r 61 | Step 0. If X < 0, create a NaN and raise the invalid operation
62 | flag. Otherwise, save FPCR i 62 | flag. Otherwise, save FPCR in D1; set FpCR to default.
63 | Notes: Default means round-to-neare 63 | Notes: Default means round-to-nearest mode, no floating-point
64 | traps, and precision control 64 | traps, and precision control = double extended.
65 | 65 |
66 | Step 1. Call slognd to obtain Y = lo 66 | Step 1. Call slognd to obtain Y = log(X), the natural log of X.
67 | Notes: Even if X is denormalized, l 67 | Notes: Even if X is denormalized, log(X) is always normalized.
68 | 68 |
69 | Step 2. Compute log_10(X) = log(X) * 69 | Step 2. Compute log_10(X) = log(X) * (1/log(2)).
70 | 2.1 Restore the user FPCR 70 | 2.1 Restore the user FPCR
71 | 2.2 Return ans := Y * INV_L2. 71 | 2.2 Return ans := Y * INV_L2.
72 | 72 |
73 | 73 |
74 | sLog2: 74 | sLog2:
75 | 75 |
76 | Step 0. If X < 0, create a NaN and r 76 | Step 0. If X < 0, create a NaN and raise the invalid operation
77 | flag. Otherwise, save FPCR i 77 | flag. Otherwise, save FPCR in D1; set FpCR to default.
78 | Notes: Default means round-to-neare 78 | Notes: Default means round-to-nearest mode, no floating-point
79 | traps, and precision control 79 | traps, and precision control = double extended.
80 | 80 |
81 | Step 1. If X is not an integer power 81 | Step 1. If X is not an integer power of two, i.e., X != 2^k,
82 | go to Step 3. 82 | go to Step 3.
83 | 83 |
84 | Step 2. Return k. 84 | Step 2. Return k.
85 | 2.1 Get integer k, X = 2^k. 85 | 2.1 Get integer k, X = 2^k.
86 | 2.2 Restore the user FPCR. 86 | 2.2 Restore the user FPCR.
87 | 2.3 Return ans := convert-to-dou 87 | 2.3 Return ans := convert-to-double-extended(k).
88 | 88 |
89 | Step 3. Call sLogN to obtain Y = log 89 | Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
90 | 90 |
91 | Step 4. Compute log_2(X) = log(X) * 91 | Step 4. Compute log_2(X) = log(X) * (1/log(2)).
92 | 4.1 Restore the user FPCR 92 | 4.1 Restore the user FPCR
93 | 4.2 Return ans := Y * INV_L2. 93 | 4.2 Return ans := Y * INV_L2.
94 | 94 |
95 95
96 | Copyright (C) Motorola, Inc. 1 96 | Copyright (C) Motorola, Inc. 1990
97 | All Rights Reserved 97 | All Rights Reserved
98 | 98 |
99 | For details on the license for this fi !! 99 | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
100 | file, README, in this same directory. !! 100 | The copyright notice above does not evidence any
>> 101 | actual or intended publication of such source code.
101 102
102 |SLOG2 idnt 2,1 | Motorola 040 Floating 103 |SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package
103 104
104 |section 8 105 |section 8
105 106
106 |xref t_frcinx !! 107 |xref t_frcinx
107 |xref t_operr 108 |xref t_operr
108 |xref slogn 109 |xref slogn
109 |xref slognd 110 |xref slognd
110 111
111 INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x372871 112 INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
112 113
113 INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0 114 INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
114 115
115 .global slog10d 116 .global slog10d
116 slog10d: 117 slog10d:
117 |--entry point for Log10(X), X is denormalized 118 |--entry point for Log10(X), X is denormalized
118 movel (%a0),%d0 119 movel (%a0),%d0
119 blt invalid 120 blt invalid
120 movel %d1,-(%sp) 121 movel %d1,-(%sp)
121 clrl %d1 122 clrl %d1
122 bsr slognd 123 bsr slognd | ...log(X), X denorm.
123 fmovel (%sp)+,%fpcr 124 fmovel (%sp)+,%fpcr
124 fmulx INV_L10,%fp0 125 fmulx INV_L10,%fp0
125 bra t_frcinx 126 bra t_frcinx
126 127
127 .global slog10 128 .global slog10
128 slog10: 129 slog10:
129 |--entry point for Log10(X), X is normalized 130 |--entry point for Log10(X), X is normalized
130 131
131 movel (%a0),%d0 132 movel (%a0),%d0
132 blt invalid 133 blt invalid
133 movel %d1,-(%sp) 134 movel %d1,-(%sp)
134 clrl %d1 135 clrl %d1
135 bsr slogn 136 bsr slogn | ...log(X), X normal.
136 fmovel (%sp)+,%fpcr 137 fmovel (%sp)+,%fpcr
137 fmulx INV_L10,%fp0 138 fmulx INV_L10,%fp0
138 bra t_frcinx 139 bra t_frcinx
139 140
140 141
141 .global slog2d 142 .global slog2d
142 slog2d: 143 slog2d:
143 |--entry point for Log2(X), X is denormalized 144 |--entry point for Log2(X), X is denormalized
144 145
145 movel (%a0),%d0 146 movel (%a0),%d0
146 blt invalid 147 blt invalid
147 movel %d1,-(%sp) 148 movel %d1,-(%sp)
148 clrl %d1 149 clrl %d1
149 bsr slognd 150 bsr slognd | ...log(X), X denorm.
150 fmovel (%sp)+,%fpcr 151 fmovel (%sp)+,%fpcr
151 fmulx INV_L2,%fp0 152 fmulx INV_L2,%fp0
152 bra t_frcinx 153 bra t_frcinx
153 154
154 .global slog2 155 .global slog2
155 slog2: 156 slog2:
156 |--entry point for Log2(X), X is normalized 157 |--entry point for Log2(X), X is normalized
157 movel (%a0),%d0 158 movel (%a0),%d0
158 blt invalid 159 blt invalid
159 160
160 movel 8(%a0),%d0 161 movel 8(%a0),%d0
161 bnes continue 162 bnes continue | ...X is not 2^k
162 163
163 movel 4(%a0),%d0 164 movel 4(%a0),%d0
164 andl #0x7FFFFFFF,%d0 165 andl #0x7FFFFFFF,%d0
165 tstl %d0 166 tstl %d0
166 bnes continue 167 bnes continue
167 168
168 |--X = 2^k. 169 |--X = 2^k.
169 movew (%a0),%d0 170 movew (%a0),%d0
170 andl #0x00007FFF,%d0 171 andl #0x00007FFF,%d0
171 subl #0x3FFF,%d0 172 subl #0x3FFF,%d0
172 fmovel %d1,%fpcr 173 fmovel %d1,%fpcr
173 fmovel %d0,%fp0 174 fmovel %d0,%fp0
174 bra t_frcinx 175 bra t_frcinx
175 176
176 continue: 177 continue:
177 movel %d1,-(%sp) 178 movel %d1,-(%sp)
178 clrl %d1 179 clrl %d1
179 bsr slogn 180 bsr slogn | ...log(X), X normal.
180 fmovel (%sp)+,%fpcr 181 fmovel (%sp)+,%fpcr
181 fmulx INV_L2,%fp0 182 fmulx INV_L2,%fp0
182 bra t_frcinx 183 bra t_frcinx
183 184
184 invalid: 185 invalid:
185 bra t_operr 186 bra t_operr
186 187
187 |end 188 |end
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.