summaryrefslogtreecommitdiff
path: root/arch/m68k/fpsp040/slog2.S
blob: 517fa45632463772b3b42d27d4a84267df4b3026 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
|	slog2.sa 3.1 12/10/90
|
|       The entry point slog10 computes the base-10
|	logarithm of an input argument X.
|	slog10d does the same except the input value is a
|	denormalized number.
|	sLog2 and sLog2d are the base-2 analogues.
|
|       INPUT:	Double-extended value in memory location pointed to
|		by address register a0.
|
|       OUTPUT: log_10(X) or log_2(X) returned in floating-point
|		register fp0.
|
|       ACCURACY and MONOTONICITY: The returned result is within 1.7
|		ulps in 64 significant bit, i.e. within 0.5003 ulp
|		to 53 bits if the result is subsequently rounded
|		to double precision. The result is provably monotonic
|		in double precision.
|
|       SPEED:	Two timings are measured, both in the copy-back mode.
|		The first one is measured when the function is invoked
|		the first time (so the instructions and data are not
|		in cache), and the second one is measured when the
|		function is reinvoked at the same input argument.
|
|       ALGORITHM and IMPLEMENTATION NOTES:
|
|       slog10d:
|
|       Step 0.   If X < 0, create a NaN and raise the invalid operation
|                 flag. Otherwise, save FPCR in D1; set FpCR to default.
|       Notes:    Default means round-to-nearest mode, no floating-point
|                 traps, and precision control = double extended.
|
|       Step 1.   Call slognd to obtain Y = log(X), the natural log of X.
|       Notes:    Even if X is denormalized, log(X) is always normalized.
|
|       Step 2.   Compute log_10(X) = log(X) * (1/log(10)).
|            2.1  Restore the user FPCR
|            2.2  Return ans := Y * INV_L10.
|
|
|       slog10:
|
|       Step 0.   If X < 0, create a NaN and raise the invalid operation
|                 flag. Otherwise, save FPCR in D1; set FpCR to default.
|       Notes:    Default means round-to-nearest mode, no floating-point
|                 traps, and precision control = double extended.
|
|       Step 1.   Call sLogN to obtain Y = log(X), the natural log of X.
|
|       Step 2.   Compute log_10(X) = log(X) * (1/log(10)).
|            2.1  Restore the user FPCR
|            2.2  Return ans := Y * INV_L10.
|
|
|       sLog2d:
|
|       Step 0.   If X < 0, create a NaN and raise the invalid operation
|                 flag. Otherwise, save FPCR in D1; set FpCR to default.
|       Notes:    Default means round-to-nearest mode, no floating-point
|                 traps, and precision control = double extended.
|
|       Step 1.   Call slognd to obtain Y = log(X), the natural log of X.
|       Notes:    Even if X is denormalized, log(X) is always normalized.
|
|       Step 2.   Compute log_10(X) = log(X) * (1/log(2)).
|            2.1  Restore the user FPCR
|            2.2  Return ans := Y * INV_L2.
|
|
|       sLog2:
|
|       Step 0.   If X < 0, create a NaN and raise the invalid operation
|                 flag. Otherwise, save FPCR in D1; set FpCR to default.
|       Notes:    Default means round-to-nearest mode, no floating-point
|                 traps, and precision control = double extended.
|
|       Step 1.   If X is not an integer power of two, i.e., X != 2^k,
|                 go to Step 3.
|
|       Step 2.   Return k.
|            2.1  Get integer k, X = 2^k.
|            2.2  Restore the user FPCR.
|            2.3  Return ans := convert-to-double-extended(k).
|
|       Step 3.   Call sLogN to obtain Y = log(X), the natural log of X.
|
|       Step 4.   Compute log_2(X) = log(X) * (1/log(2)).
|            4.1  Restore the user FPCR
|            4.2  Return ans := Y * INV_L2.
|

|		Copyright (C) Motorola, Inc. 1990
|			All Rights Reserved
|
|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|	The copyright notice above does not evidence any
|	actual or intended publication of such source code.

|SLOG2    idnt    2,1 | Motorola 040 Floating Point Software Package

	|section	8

	|xref	t_frcinx
	|xref	t_operr
	|xref	slogn
	|xref	slognd

INV_L10:  .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000

INV_L2:   .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000

	.global	slog10d
slog10d:
|--entry point for Log10(X), X is denormalized
	movel		(%a0),%d0
	blt		invalid
	movel		%d1,-(%sp)
	clrl		%d1
	bsr		slognd			| ...log(X), X denorm.
	fmovel		(%sp)+,%fpcr
	fmulx		INV_L10,%fp0
	bra		t_frcinx

	.global	slog10
slog10:
|--entry point for Log10(X), X is normalized

	movel		(%a0),%d0
	blt		invalid
	movel		%d1,-(%sp)
	clrl		%d1
	bsr		slogn			| ...log(X), X normal.
	fmovel		(%sp)+,%fpcr
	fmulx		INV_L10,%fp0
	bra		t_frcinx


	.global	slog2d
slog2d:
|--entry point for Log2(X), X is denormalized

	movel		(%a0),%d0
	blt		invalid
	movel		%d1,-(%sp)
	clrl		%d1
	bsr		slognd			| ...log(X), X denorm.
	fmovel		(%sp)+,%fpcr
	fmulx		INV_L2,%fp0
	bra		t_frcinx

	.global	slog2
slog2:
|--entry point for Log2(X), X is normalized
	movel		(%a0),%d0
	blt		invalid

	movel		8(%a0),%d0
	bnes		continue		| ...X is not 2^k

	movel		4(%a0),%d0
	andl		#0x7FFFFFFF,%d0
	tstl		%d0
	bnes		continue

|--X = 2^k.
	movew		(%a0),%d0
	andl		#0x00007FFF,%d0
	subl		#0x3FFF,%d0
	fmovel		%d1,%fpcr
	fmovel		%d0,%fp0
	bra		t_frcinx

continue:
	movel		%d1,-(%sp)
	clrl		%d1
	bsr		slogn			| ...log(X), X normal.
	fmovel		(%sp)+,%fpcr
	fmulx		INV_L2,%fp0
	bra		t_frcinx

invalid:
	bra		t_operr

	|end