Annotation of sys/arch/m68k/fpsp/slog2.sa, Revision 1.1.1.1
1.1 nbrk 1: * $OpenBSD: slog2.sa,v 1.2 1996/05/29 21:05:39 niklas Exp $
2: * $NetBSD: slog2.sa,v 1.2 1994/10/26 07:49:52 cgd Exp $
3:
4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
5: * M68000 Hi-Performance Microprocessor Division
6: * M68040 Software Package
7: *
8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
9: * All rights reserved.
10: *
11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
12: * To the maximum extent permitted by applicable law,
13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
15: * PARTICULAR PURPOSE and any warranty against infringement with
16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
17: * and any accompanying written materials.
18: *
19: * To the maximum extent permitted by applicable law,
20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
25: * and support of the SOFTWARE.
26: *
27: * You are hereby granted a copyright license to use, modify, and
28: * distribute the SOFTWARE so long as this entire notice is retained
29: * without alteration in any modified and/or redistributed versions,
30: * and that such modified versions are clearly identified as such.
31: * No licenses are granted by implication, estoppel or otherwise
32: * under any patents or trademarks of Motorola, Inc.
33:
34: *
35: * slog2.sa 3.1 12/10/90
36: *
37: * The entry point slog10 computes the base-10
38: * logarithm of an input argument X.
39: * slog10d does the same except the input value is a
40: * denormalized number.
41: * sLog2 and sLog2d are the base-2 analogues.
42: *
43: * INPUT: Double-extended value in memory location pointed to
44: * by address register a0.
45: *
46: * OUTPUT: log_10(X) or log_2(X) returned in floating-point
47: * register fp0.
48: *
49: * ACCURACY and MONOTONICITY: The returned result is within 1.7
50: * ulps in 64 significant bit, i.e. within 0.5003 ulp
51: * to 53 bits if the result is subsequently rounded
52: * to double precision. The result is provably monotonic
53: * in double precision.
54: *
55: * SPEED: Two timings are measured, both in the copy-back mode.
56: * The first one is measured when the function is invoked
57: * the first time (so the instructions and data are not
58: * in cache), and the second one is measured when the
59: * function is reinvoked at the same input argument.
60: *
61: * ALGORITHM and IMPLEMENTATION NOTES:
62: *
63: * slog10d:
64: *
65: * Step 0. If X < 0, create a NaN and raise the invalid operation
66: * flag. Otherwise, save FPCR in D1; set FpCR to default.
67: * Notes: Default means round-to-nearest mode, no floating-point
68: * traps, and precision control = double extended.
69: *
70: * Step 1. Call slognd to obtain Y = log(X), the natural log of X.
71: * Notes: Even if X is denormalized, log(X) is always normalized.
72: *
73: * Step 2. Compute log_10(X) = log(X) * (1/log(10)).
74: * 2.1 Restore the user FPCR
75: * 2.2 Return ans := Y * INV_L10.
76: *
77: *
78: * slog10:
79: *
80: * Step 0. If X < 0, create a NaN and raise the invalid operation
81: * flag. Otherwise, save FPCR in D1; set FpCR to default.
82: * Notes: Default means round-to-nearest mode, no floating-point
83: * traps, and precision control = double extended.
84: *
85: * Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
86: *
87: * Step 2. Compute log_10(X) = log(X) * (1/log(10)).
88: * 2.1 Restore the user FPCR
89: * 2.2 Return ans := Y * INV_L10.
90: *
91: *
92: * sLog2d:
93: *
94: * Step 0. If X < 0, create a NaN and raise the invalid operation
95: * flag. Otherwise, save FPCR in D1; set FpCR to default.
96: * Notes: Default means round-to-nearest mode, no floating-point
97: * traps, and precision control = double extended.
98: *
99: * Step 1. Call slognd to obtain Y = log(X), the natural log of X.
100: * Notes: Even if X is denormalized, log(X) is always normalized.
101: *
102: * Step 2. Compute log_10(X) = log(X) * (1/log(2)).
103: * 2.1 Restore the user FPCR
104: * 2.2 Return ans := Y * INV_L2.
105: *
106: *
107: * sLog2:
108: *
109: * Step 0. If X < 0, create a NaN and raise the invalid operation
110: * flag. Otherwise, save FPCR in D1; set FpCR to default.
111: * Notes: Default means round-to-nearest mode, no floating-point
112: * traps, and precision control = double extended.
113: *
114: * Step 1. If X is not an integer power of two, i.e., X != 2^k,
115: * go to Step 3.
116: *
117: * Step 2. Return k.
118: * 2.1 Get integer k, X = 2^k.
119: * 2.2 Restore the user FPCR.
120: * 2.3 Return ans := convert-to-double-extended(k).
121: *
122: * Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
123: *
124: * Step 4. Compute log_2(X) = log(X) * (1/log(2)).
125: * 4.1 Restore the user FPCR
126: * 4.2 Return ans := Y * INV_L2.
127: *
128:
129: SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package
130:
131: section 8
132:
133: xref t_frcinx
134: xref t_operr
135: xref slogn
136: xref slognd
137:
138: INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000
139:
140: INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000
141:
142: xdef slog10d
143: slog10d:
144: *--entry point for Log10(X), X is denormalized
145: move.l (a0),d0
146: blt.w invalid
147: move.l d1,-(sp)
148: clr.l d1
149: bsr slognd ...log(X), X denorm.
150: fmove.l (sp)+,fpcr
151: fmul.x INV_L10,fp0
152: bra t_frcinx
153:
154: xdef slog10
155: slog10:
156: *--entry point for Log10(X), X is normalized
157:
158: move.l (a0),d0
159: blt.w invalid
160: move.l d1,-(sp)
161: clr.l d1
162: bsr slogn ...log(X), X normal.
163: fmove.l (sp)+,fpcr
164: fmul.x INV_L10,fp0
165: bra t_frcinx
166:
167:
168: xdef slog2d
169: slog2d:
170: *--entry point for Log2(X), X is denormalized
171:
172: move.l (a0),d0
173: blt.w invalid
174: move.l d1,-(sp)
175: clr.l d1
176: bsr slognd ...log(X), X denorm.
177: fmove.l (sp)+,fpcr
178: fmul.x INV_L2,fp0
179: bra t_frcinx
180:
181: xdef slog2
182: slog2:
183: *--entry point for Log2(X), X is normalized
184: move.l (a0),d0
185: blt.w invalid
186:
187: move.l 8(a0),d0
188: bne.b continue ...X is not 2^k
189:
190: move.l 4(a0),d0
191: and.l #$7FFFFFFF,d0
192: tst.l d0
193: bne.b continue
194:
195: *--X = 2^k.
196: move.w (a0),d0
197: and.l #$00007FFF,d0
198: sub.l #$3FFF,d0
199: fmove.l d1,fpcr
200: fmove.l d0,fp0
201: bra t_frcinx
202:
203: continue:
204: move.l d1,-(sp)
205: clr.l d1
206: bsr slogn ...log(X), X normal.
207: fmove.l (sp)+,fpcr
208: fmul.x INV_L2,fp0
209: bra t_frcinx
210:
211: invalid:
212: bra t_operr
213:
214: end
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