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 | For details on the license for this file, please see the
100 | file, README, in this same directory. 100 | file, README, in this same directory.
101 101
102 |SLOG2 idnt 2,1 | Motorola 040 Floating 102 |SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package
103 103
104 |section 8 104 |section 8
105 105
106 |xref t_frcinx 106 |xref t_frcinx
107 |xref t_operr 107 |xref t_operr
108 |xref slogn 108 |xref slogn
109 |xref slognd 109 |xref slognd
110 110
111 INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x372871 111 INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
112 112
113 INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0 113 INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
114 114
115 .global slog10d 115 .global slog10d
116 slog10d: 116 slog10d:
117 |--entry point for Log10(X), X is denormalized 117 |--entry point for Log10(X), X is denormalized
118 movel (%a0),%d0 118 movel (%a0),%d0
119 blt invalid 119 blt invalid
120 movel %d1,-(%sp) 120 movel %d1,-(%sp)
121 clrl %d1 121 clrl %d1
122 bsr slognd 122 bsr slognd | ...log(X), X denorm.
123 fmovel (%sp)+,%fpcr 123 fmovel (%sp)+,%fpcr
124 fmulx INV_L10,%fp0 124 fmulx INV_L10,%fp0
125 bra t_frcinx 125 bra t_frcinx
126 126
127 .global slog10 127 .global slog10
128 slog10: 128 slog10:
129 |--entry point for Log10(X), X is normalized 129 |--entry point for Log10(X), X is normalized
130 130
131 movel (%a0),%d0 131 movel (%a0),%d0
132 blt invalid 132 blt invalid
133 movel %d1,-(%sp) 133 movel %d1,-(%sp)
134 clrl %d1 134 clrl %d1
135 bsr slogn 135 bsr slogn | ...log(X), X normal.
136 fmovel (%sp)+,%fpcr 136 fmovel (%sp)+,%fpcr
137 fmulx INV_L10,%fp0 137 fmulx INV_L10,%fp0
138 bra t_frcinx 138 bra t_frcinx
139 139
140 140
141 .global slog2d 141 .global slog2d
142 slog2d: 142 slog2d:
143 |--entry point for Log2(X), X is denormalized 143 |--entry point for Log2(X), X is denormalized
144 144
145 movel (%a0),%d0 145 movel (%a0),%d0
146 blt invalid 146 blt invalid
147 movel %d1,-(%sp) 147 movel %d1,-(%sp)
148 clrl %d1 148 clrl %d1
149 bsr slognd 149 bsr slognd | ...log(X), X denorm.
150 fmovel (%sp)+,%fpcr 150 fmovel (%sp)+,%fpcr
151 fmulx INV_L2,%fp0 151 fmulx INV_L2,%fp0
152 bra t_frcinx 152 bra t_frcinx
153 153
154 .global slog2 154 .global slog2
155 slog2: 155 slog2:
156 |--entry point for Log2(X), X is normalized 156 |--entry point for Log2(X), X is normalized
157 movel (%a0),%d0 157 movel (%a0),%d0
158 blt invalid 158 blt invalid
159 159
160 movel 8(%a0),%d0 160 movel 8(%a0),%d0
161 bnes continue 161 bnes continue | ...X is not 2^k
162 162
163 movel 4(%a0),%d0 163 movel 4(%a0),%d0
164 andl #0x7FFFFFFF,%d0 164 andl #0x7FFFFFFF,%d0
165 tstl %d0 165 tstl %d0
166 bnes continue 166 bnes continue
167 167
168 |--X = 2^k. 168 |--X = 2^k.
169 movew (%a0),%d0 169 movew (%a0),%d0
170 andl #0x00007FFF,%d0 170 andl #0x00007FFF,%d0
171 subl #0x3FFF,%d0 171 subl #0x3FFF,%d0
172 fmovel %d1,%fpcr 172 fmovel %d1,%fpcr
173 fmovel %d0,%fp0 173 fmovel %d0,%fp0
174 bra t_frcinx 174 bra t_frcinx
175 175
176 continue: 176 continue:
177 movel %d1,-(%sp) 177 movel %d1,-(%sp)
178 clrl %d1 178 clrl %d1
179 bsr slogn 179 bsr slogn | ...log(X), X normal.
180 fmovel (%sp)+,%fpcr 180 fmovel (%sp)+,%fpcr
181 fmulx INV_L2,%fp0 181 fmulx INV_L2,%fp0
182 bra t_frcinx 182 bra t_frcinx
183 183
184 invalid: 184 invalid:
185 bra t_operr 185 bra t_operr
186 186
187 |end 187 |end
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