xref: /netbsd-src/sys/arch/m68k/fpe/fpu_log.c (revision 8b0f9554ff8762542c4defc4f70e1eb76fb508fa)
1 /*	$NetBSD: fpu_log.c,v 1.9 2005/12/11 12:17:52 christos Exp $	*/
2 
3 /*
4  * Copyright (c) 1995  Ken Nakata
5  *	All rights reserved.
6  *
7  * Redistribution and use in source and binary forms, with or without
8  * modification, are permitted provided that the following conditions
9  * are met:
10  * 1. Redistributions of source code must retain the above copyright
11  *    notice, this list of conditions and the following disclaimer.
12  * 2. Redistributions in binary form must reproduce the above copyright
13  *    notice, this list of conditions and the following disclaimer in the
14  *    documentation and/or other materials provided with the distribution.
15  * 3. Neither the name of the author nor the names of its contributors
16  *    may be used to endorse or promote products derived from this software
17  *    without specific prior written permission.
18  *
19  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
20  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
23  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29  * SUCH DAMAGE.
30  *
31  *	@(#)fpu_log.c	10/8/95
32  */
33 
34 #include <sys/cdefs.h>
35 __KERNEL_RCSID(0, "$NetBSD: fpu_log.c,v 1.9 2005/12/11 12:17:52 christos Exp $");
36 
37 #include <sys/types.h>
38 #include <sys/systm.h>
39 
40 #include "fpu_emulate.h"
41 
42 static u_int logA6[] = { 0x3FC2499A, 0xB5E4040B };
43 static u_int logA5[] = { 0xBFC555B5, 0x848CB7DB };
44 static u_int logA4[] = { 0x3FC99999, 0x987D8730 };
45 static u_int logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 };
46 static u_int logA2[] = { 0x3FD55555, 0x555555A4 };
47 static u_int logA1[] = { 0xBFE00000, 0x00000008 };
48 
49 static u_int logB5[] = { 0x3F175496, 0xADD7DAD6 };
50 static u_int logB4[] = { 0x3F3C71C2, 0xFE80C7E0 };
51 static u_int logB3[] = { 0x3F624924, 0x928BCCFF };
52 static u_int logB2[] = { 0x3F899999, 0x999995EC };
53 static u_int logB1[] = { 0x3FB55555, 0x55555555 };
54 
55 /* sfpn = shortened fp number; can represent only positive numbers */
56 static struct sfpn {
57     int		sp_exp;
58     u_int	sp_m0, sp_m1;
59 } logtbl[] = {
60     { 0x3FFE - 0x3fff, 0xFE03F80FU, 0xE03F80FEU },
61     { 0x3FF7 - 0x3fff, 0xFF015358U, 0x833C47E2U },
62     { 0x3FFE - 0x3fff, 0xFA232CF2U, 0x52138AC0U },
63     { 0x3FF9 - 0x3fff, 0xBDC8D83EU, 0xAD88D549U },
64     { 0x3FFE - 0x3fff, 0xF6603D98U, 0x0F6603DAU },
65     { 0x3FFA - 0x3fff, 0x9CF43DCFU, 0xF5EAFD48U },
66     { 0x3FFE - 0x3fff, 0xF2B9D648U, 0x0F2B9D65U },
67     { 0x3FFA - 0x3fff, 0xDA16EB88U, 0xCB8DF614U },
68     { 0x3FFE - 0x3fff, 0xEF2EB71FU, 0xC4345238U },
69     { 0x3FFB - 0x3fff, 0x8B29B775U, 0x1BD70743U },
70     { 0x3FFE - 0x3fff, 0xEBBDB2A5U, 0xC1619C8CU },
71     { 0x3FFB - 0x3fff, 0xA8D839F8U, 0x30C1FB49U },
72     { 0x3FFE - 0x3fff, 0xE865AC7BU, 0x7603A197U },
73     { 0x3FFB - 0x3fff, 0xC61A2EB1U, 0x8CD907ADU },
74     { 0x3FFE - 0x3fff, 0xE525982AU, 0xF70C880EU },
75     { 0x3FFB - 0x3fff, 0xE2F2A47AU, 0xDE3A18AFU },
76     { 0x3FFE - 0x3fff, 0xE1FC780EU, 0x1FC780E2U },
77     { 0x3FFB - 0x3fff, 0xFF64898EU, 0xDF55D551U },
78     { 0x3FFE - 0x3fff, 0xDEE95C4CU, 0xA037BA57U },
79     { 0x3FFC - 0x3fff, 0x8DB956A9U, 0x7B3D0148U },
80     { 0x3FFE - 0x3fff, 0xDBEB61EEU, 0xD19C5958U },
81     { 0x3FFC - 0x3fff, 0x9B8FE100U, 0xF47BA1DEU },
82     { 0x3FFE - 0x3fff, 0xD901B203U, 0x6406C80EU },
83     { 0x3FFC - 0x3fff, 0xA9372F1DU, 0x0DA1BD17U },
84     { 0x3FFE - 0x3fff, 0xD62B80D6U, 0x2B80D62CU },
85     { 0x3FFC - 0x3fff, 0xB6B07F38U, 0xCE90E46BU },
86     { 0x3FFE - 0x3fff, 0xD3680D36U, 0x80D3680DU },
87     { 0x3FFC - 0x3fff, 0xC3FD0329U, 0x06488481U },
88     { 0x3FFE - 0x3fff, 0xD0B69FCBU, 0xD2580D0BU },
89     { 0x3FFC - 0x3fff, 0xD11DE0FFU, 0x15AB18CAU },
90     { 0x3FFE - 0x3fff, 0xCE168A77U, 0x25080CE1U },
91     { 0x3FFC - 0x3fff, 0xDE1433A1U, 0x6C66B150U },
92     { 0x3FFE - 0x3fff, 0xCB8727C0U, 0x65C393E0U },
93     { 0x3FFC - 0x3fff, 0xEAE10B5AU, 0x7DDC8ADDU },
94     { 0x3FFE - 0x3fff, 0xC907DA4EU, 0x871146ADU },
95     { 0x3FFC - 0x3fff, 0xF7856E5EU, 0xE2C9B291U },
96     { 0x3FFE - 0x3fff, 0xC6980C69U, 0x80C6980CU },
97     { 0x3FFD - 0x3fff, 0x82012CA5U, 0xA68206D7U },
98     { 0x3FFE - 0x3fff, 0xC4372F85U, 0x5D824CA6U },
99     { 0x3FFD - 0x3fff, 0x882C5FCDU, 0x7256A8C5U },
100     { 0x3FFE - 0x3fff, 0xC1E4BBD5U, 0x95F6E947U },
101     { 0x3FFD - 0x3fff, 0x8E44C60BU, 0x4CCFD7DEU },
102     { 0x3FFE - 0x3fff, 0xBFA02FE8U, 0x0BFA02FFU },
103     { 0x3FFD - 0x3fff, 0x944AD09EU, 0xF4351AF6U },
104     { 0x3FFE - 0x3fff, 0xBD691047U, 0x07661AA3U },
105     { 0x3FFD - 0x3fff, 0x9A3EECD4U, 0xC3EAA6B2U },
106     { 0x3FFE - 0x3fff, 0xBB3EE721U, 0xA54D880CU },
107     { 0x3FFD - 0x3fff, 0xA0218434U, 0x353F1DE8U },
108     { 0x3FFE - 0x3fff, 0xB92143FAU, 0x36F5E02EU },
109     { 0x3FFD - 0x3fff, 0xA5F2FCABU, 0xBBC506DAU },
110     { 0x3FFE - 0x3fff, 0xB70FBB5AU, 0x19BE3659U },
111     { 0x3FFD - 0x3fff, 0xABB3B8BAU, 0x2AD362A5U },
112     { 0x3FFE - 0x3fff, 0xB509E68AU, 0x9B94821FU },
113     { 0x3FFD - 0x3fff, 0xB1641795U, 0xCE3CA97BU },
114     { 0x3FFE - 0x3fff, 0xB30F6352U, 0x8917C80BU },
115     { 0x3FFD - 0x3fff, 0xB7047551U, 0x5D0F1C61U },
116     { 0x3FFE - 0x3fff, 0xB11FD3B8U, 0x0B11FD3CU },
117     { 0x3FFD - 0x3fff, 0xBC952AFEU, 0xEA3D13E1U },
118     { 0x3FFE - 0x3fff, 0xAF3ADDC6U, 0x80AF3ADEU },
119     { 0x3FFD - 0x3fff, 0xC2168ED0U, 0xF458BA4AU },
120     { 0x3FFE - 0x3fff, 0xAD602B58U, 0x0AD602B6U },
121     { 0x3FFD - 0x3fff, 0xC788F439U, 0xB3163BF1U },
122     { 0x3FFE - 0x3fff, 0xAB8F69E2U, 0x8359CD11U },
123     { 0x3FFD - 0x3fff, 0xCCECAC08U, 0xBF04565DU },
124     { 0x3FFE - 0x3fff, 0xA9C84A47U, 0xA07F5638U },
125     { 0x3FFD - 0x3fff, 0xD2420487U, 0x2DD85160U },
126     { 0x3FFE - 0x3fff, 0xA80A80A8U, 0x0A80A80BU },
127     { 0x3FFD - 0x3fff, 0xD7894992U, 0x3BC3588AU },
128     { 0x3FFE - 0x3fff, 0xA655C439U, 0x2D7B73A8U },
129     { 0x3FFD - 0x3fff, 0xDCC2C4B4U, 0x9887DACCU },
130     { 0x3FFE - 0x3fff, 0xA4A9CF1DU, 0x96833751U },
131     { 0x3FFD - 0x3fff, 0xE1EEBD3EU, 0x6D6A6B9EU },
132     { 0x3FFE - 0x3fff, 0xA3065E3FU, 0xAE7CD0E0U },
133     { 0x3FFD - 0x3fff, 0xE70D785CU, 0x2F9F5BDCU },
134     { 0x3FFE - 0x3fff, 0xA16B312EU, 0xA8FC377DU },
135     { 0x3FFD - 0x3fff, 0xEC1F392CU, 0x5179F283U },
136     { 0x3FFE - 0x3fff, 0x9FD809FDU, 0x809FD80AU },
137     { 0x3FFD - 0x3fff, 0xF12440D3U, 0xE36130E6U },
138     { 0x3FFE - 0x3fff, 0x9E4CAD23U, 0xDD5F3A20U },
139     { 0x3FFD - 0x3fff, 0xF61CCE92U, 0x346600BBU },
140     { 0x3FFE - 0x3fff, 0x9CC8E160U, 0xC3FB19B9U },
141     { 0x3FFD - 0x3fff, 0xFB091FD3U, 0x8145630AU },
142     { 0x3FFE - 0x3fff, 0x9B4C6F9EU, 0xF03A3CAAU },
143     { 0x3FFD - 0x3fff, 0xFFE97042U, 0xBFA4C2ADU },
144     { 0x3FFE - 0x3fff, 0x99D722DAU, 0xBDE58F06U },
145     { 0x3FFE - 0x3fff, 0x825EFCEDU, 0x49369330U },
146     { 0x3FFE - 0x3fff, 0x9868C809U, 0x868C8098U },
147     { 0x3FFE - 0x3fff, 0x84C37A7AU, 0xB9A905C9U },
148     { 0x3FFE - 0x3fff, 0x97012E02U, 0x5C04B809U },
149     { 0x3FFE - 0x3fff, 0x87224C2EU, 0x8E645FB7U },
150     { 0x3FFE - 0x3fff, 0x95A02568U, 0x095A0257U },
151     { 0x3FFE - 0x3fff, 0x897B8CACU, 0x9F7DE298U },
152     { 0x3FFE - 0x3fff, 0x94458094U, 0x45809446U },
153     { 0x3FFE - 0x3fff, 0x8BCF55DEU, 0xC4CD05FEU },
154     { 0x3FFE - 0x3fff, 0x92F11384U, 0x0497889CU },
155     { 0x3FFE - 0x3fff, 0x8E1DC0FBU, 0x89E125E5U },
156     { 0x3FFE - 0x3fff, 0x91A2B3C4U, 0xD5E6F809U },
157     { 0x3FFE - 0x3fff, 0x9066E68CU, 0x955B6C9BU },
158     { 0x3FFE - 0x3fff, 0x905A3863U, 0x3E06C43BU },
159     { 0x3FFE - 0x3fff, 0x92AADE74U, 0xC7BE59E0U },
160     { 0x3FFE - 0x3fff, 0x8F1779D9U, 0xFDC3A219U },
161     { 0x3FFE - 0x3fff, 0x94E9BFF6U, 0x15845643U },
162     { 0x3FFE - 0x3fff, 0x8DDA5202U, 0x37694809U },
163     { 0x3FFE - 0x3fff, 0x9723A1B7U, 0x20134203U },
164     { 0x3FFE - 0x3fff, 0x8CA29C04U, 0x6514E023U },
165     { 0x3FFE - 0x3fff, 0x995899C8U, 0x90EB8990U },
166     { 0x3FFE - 0x3fff, 0x8B70344AU, 0x139BC75AU },
167     { 0x3FFE - 0x3fff, 0x9B88BDAAU, 0x3A3DAE2FU },
168     { 0x3FFE - 0x3fff, 0x8A42F870U, 0x5669DB46U },
169     { 0x3FFE - 0x3fff, 0x9DB4224FU, 0xFFE1157CU },
170     { 0x3FFE - 0x3fff, 0x891AC73AU, 0xE9819B50U },
171     { 0x3FFE - 0x3fff, 0x9FDADC26U, 0x8B7A12DAU },
172     { 0x3FFE - 0x3fff, 0x87F78087U, 0xF78087F8U },
173     { 0x3FFE - 0x3fff, 0xA1FCFF17U, 0xCE733BD4U },
174     { 0x3FFE - 0x3fff, 0x86D90544U, 0x7A34ACC6U },
175     { 0x3FFE - 0x3fff, 0xA41A9E8FU, 0x5446FB9FU },
176     { 0x3FFE - 0x3fff, 0x85BF3761U, 0x2CEE3C9BU },
177     { 0x3FFE - 0x3fff, 0xA633CD7EU, 0x6771CD8BU },
178     { 0x3FFE - 0x3fff, 0x84A9F9C8U, 0x084A9F9DU },
179     { 0x3FFE - 0x3fff, 0xA8489E60U, 0x0B435A5EU },
180     { 0x3FFE - 0x3fff, 0x83993052U, 0x3FBE3368U },
181     { 0x3FFE - 0x3fff, 0xAA59233CU, 0xCCA4BD49U },
182     { 0x3FFE - 0x3fff, 0x828CBFBEU, 0xB9A020A3U },
183     { 0x3FFE - 0x3fff, 0xAC656DAEU, 0x6BCC4985U },
184     { 0x3FFE - 0x3fff, 0x81848DA8U, 0xFAF0D277U },
185     { 0x3FFE - 0x3fff, 0xAE6D8EE3U, 0x60BB2468U },
186     { 0x3FFE - 0x3fff, 0x80808080U, 0x80808081U },
187     { 0x3FFE - 0x3fff, 0xB07197A2U, 0x3C46C654U },
188 };
189 
190 static struct fpn *__fpu_logn __P((struct fpemu *fe));
191 
192 /*
193  * natural log - algorithm taken from Motorola FPSP,
194  * except this doesn't bother to check for invalid input.
195  */
196 static struct fpn *
197 __fpu_logn(fe)
198      struct fpemu *fe;
199 {
200     static struct fpn X, F, U, V, W, KLOG2;
201     struct fpn *d;
202     int i, k;
203 
204     CPYFPN(&X, &fe->fe_f2);
205 
206     /* see if |X-1| < 1/16 approx. */
207     if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) ||
208 	(0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) {
209 	/* log near 1 */
210 #if FPE_DEBUG
211 	printf("__fpu_logn: log near 1\n");
212 #endif
213 
214 	fpu_const(&fe->fe_f1, 0x32);
215 	/* X+1 */
216 	d = fpu_add(fe);
217 	CPYFPN(&V, d);
218 
219 	CPYFPN(&fe->fe_f1, &X);
220 	fpu_const(&fe->fe_f2, 0x32); /* 1.0 */
221 	fe->fe_f2.fp_sign = 1; /* -1.0 */
222 	/* X-1 */
223 	d = fpu_add(fe);
224 	CPYFPN(&fe->fe_f1, d);
225 	/* 2(X-1) */
226 	fe->fe_f1.fp_exp++; /* *= 2 */
227 	CPYFPN(&fe->fe_f2, &V);
228 	/* U=2(X-1)/(X+1) */
229 	d = fpu_div(fe);
230 	CPYFPN(&U, d);
231 	CPYFPN(&fe->fe_f1, d);
232 	CPYFPN(&fe->fe_f2, d);
233 	/* V=U*U */
234 	d = fpu_mul(fe);
235 	CPYFPN(&V, d);
236 	CPYFPN(&fe->fe_f1, d);
237 	CPYFPN(&fe->fe_f2, d);
238 	/* W=V*V */
239 	d = fpu_mul(fe);
240 	CPYFPN(&W, d);
241 
242 	/* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */
243 
244 	/* B1+W*(B3+W*B5) part */
245 	CPYFPN(&fe->fe_f1, d);
246 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5);
247 	/* W*B5 */
248 	d = fpu_mul(fe);
249 	CPYFPN(&fe->fe_f1, d);
250 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3);
251 	/* B3+W*B5 */
252 	d = fpu_add(fe);
253 	CPYFPN(&fe->fe_f1, d);
254 	CPYFPN(&fe->fe_f2, &W);
255 	/* W*(B3+W*B5) */
256 	d = fpu_mul(fe);
257 	CPYFPN(&fe->fe_f1, d);
258 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1);
259 	/* B1+W*(B3+W*B5) */
260 	d = fpu_add(fe);
261 	CPYFPN(&X, d);
262 
263 	/* [V*(B2+W*B4)] part */
264 	CPYFPN(&fe->fe_f1, &W);
265 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4);
266 	/* W*B4 */
267 	d = fpu_mul(fe);
268 	CPYFPN(&fe->fe_f1, d);
269 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2);
270 	/* B2+W*B4 */
271 	d = fpu_add(fe);
272 	CPYFPN(&fe->fe_f1, d);
273 	CPYFPN(&fe->fe_f2, &V);
274 	/* V*(B2+W*B4) */
275 	d = fpu_mul(fe);
276 	CPYFPN(&fe->fe_f1, d);
277 	CPYFPN(&fe->fe_f2, &X);
278 	/* B1+W*(B3+W*B5)+V*(B2+W*B4) */
279 	d = fpu_add(fe);
280 	CPYFPN(&fe->fe_f1, d);
281 	CPYFPN(&fe->fe_f2, &V);
282 	/* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
283 	d = fpu_mul(fe);
284 	CPYFPN(&fe->fe_f1, d);
285 	CPYFPN(&fe->fe_f2, &U);
286 	/* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
287 	d = fpu_mul(fe);
288 	CPYFPN(&fe->fe_f1, d);
289 	CPYFPN(&fe->fe_f2, &U);
290 	/* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
291 	d = fpu_add(fe);
292     } else /* the usual case */ {
293 #if FPE_DEBUG
294 	printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n",
295 	       X.fp_exp, X.fp_mant[0], X.fp_mant[1]);
296 #endif
297 
298 	k = X.fp_exp;
299 	/* X <- Y */
300 	X.fp_exp = fe->fe_f2.fp_exp = 0;
301 
302 	/* get the most significant 7 bits of X */
303 	F.fp_class = FPC_NUM;
304 	F.fp_sign = 0;
305 	F.fp_exp = X.fp_exp;
306 	F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG));
307 	F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG));
308 	F.fp_mant[1] = F.fp_mant[2] = 0;
309 	F.fp_sticky = 0;
310 
311 #if FPE_DEBUG
312 	printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n",
313 	       fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0],
314 	       fe->fe_f2.fp_mant[1], k);
315 	printf("__fpu_logn: F=(%d,%08x,%08x...)\n",
316 	       F.fp_exp, F.fp_mant[0], F.fp_mant[1]);
317 #endif
318 
319 	/* index to the table */
320 	i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e;
321 
322 #if FPE_DEBUG
323 	printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i);
324 #endif
325 
326 	CPYFPN(&fe->fe_f1, &F);
327 	/* -F */
328 	fe->fe_f1.fp_sign = 1;
329 	/* Y-F */
330 	d = fpu_add(fe);
331 	CPYFPN(&fe->fe_f1, d);
332 
333 	/* fe_f2 = 1/F */
334 	fe->fe_f2.fp_class = FPC_NUM;
335 	fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
336 	fe->fe_f2.fp_exp = logtbl[i].sp_exp;
337 	fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
338 	fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
339 	    (logtbl[i].sp_m1 >> (31 - FP_LG));
340 	fe->fe_f2.fp_mant[2] = (u_int)(logtbl[i].sp_m1 << (FP_LG + 1));
341 
342 #if FPE_DEBUG
343 	printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
344 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
345 #endif
346 
347 	/* U = (Y-F) * (1/F) */
348 	d = fpu_mul(fe);
349 	CPYFPN(&U, d);
350 
351 	/* KLOG2 = K * ln(2) */
352 	/* fe_f1 == (fpn)k */
353 	fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k);
354 	(void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
355 #if FPE_DEBUG
356 	printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", fe->fe_f1.fp_exp,
357 	       fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]);
358 	printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
359 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
360 #endif
361 	/* K * LOGOF2 */
362 	d = fpu_mul(fe);
363 	CPYFPN(&KLOG2, d);
364 
365 	/* V=U*U */
366 	CPYFPN(&fe->fe_f1, &U);
367 	CPYFPN(&fe->fe_f2, &U);
368 	d = fpu_mul(fe);
369 	CPYFPN(&V, d);
370 
371 	/*
372 	 * approximation of LOG(1+U) by
373 	 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6)))
374 	 */
375 
376 	/* (U+V*(A1+V*(A3+V*A5))) part */
377 	CPYFPN(&fe->fe_f1, d);
378 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5);
379 	/* V*A5 */
380 	d = fpu_mul(fe);
381 
382 	CPYFPN(&fe->fe_f1, d);
383 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3);
384 	/* A3+V*A5 */
385 	d = fpu_add(fe);
386 
387 	CPYFPN(&fe->fe_f1, d);
388 	CPYFPN(&fe->fe_f2, &V);
389 	/* V*(A3+V*A5) */
390 	d = fpu_mul(fe);
391 
392 	CPYFPN(&fe->fe_f1, d);
393 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1);
394 	/* A1+V*(A3+V*A5) */
395 	d = fpu_add(fe);
396 
397 	CPYFPN(&fe->fe_f1, d);
398 	CPYFPN(&fe->fe_f2, &V);
399 	/* V*(A1+V*(A3+V*A5)) */
400 	d = fpu_mul(fe);
401 
402 	CPYFPN(&fe->fe_f1, d);
403 	CPYFPN(&fe->fe_f2, &U);
404 	/* U+V*(A1+V*(A3+V*A5)) */
405 	d = fpu_add(fe);
406 
407 	CPYFPN(&X, d);
408 
409 	/* (U*V*(A2+V*(A4+V*A6))) part */
410 	CPYFPN(&fe->fe_f1, &V);
411 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6);
412 	/* V*A6 */
413 	d = fpu_mul(fe);
414 	CPYFPN(&fe->fe_f1, d);
415 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4);
416 	/* A4+V*A6 */
417 	d = fpu_add(fe);
418 	CPYFPN(&fe->fe_f1, d);
419 	CPYFPN(&fe->fe_f2, &V);
420 	/* V*(A4+V*A6) */
421 	d = fpu_mul(fe);
422 	CPYFPN(&fe->fe_f1, d);
423 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2);
424 	/* A2+V*(A4+V*A6) */
425 	d = fpu_add(fe);
426 	CPYFPN(&fe->fe_f1, d);
427 	CPYFPN(&fe->fe_f2, &V);
428 	/* V*(A2+V*(A4+V*A6)) */
429 	d = fpu_mul(fe);
430 	CPYFPN(&fe->fe_f1, d);
431 	CPYFPN(&fe->fe_f2, &U);
432 	/* U*V*(A2+V*(A4+V*A6)) */
433 	d = fpu_mul(fe);
434 	CPYFPN(&fe->fe_f1, d);
435 	i++;
436 	/* fe_f2 = logtbl[i+1] (== LOG(F)) */
437 	fe->fe_f2.fp_class = FPC_NUM;
438 	fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
439 	fe->fe_f2.fp_exp = logtbl[i].sp_exp;
440 	fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
441 	fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
442 	    (logtbl[i].sp_m1 >> (31 - FP_LG));
443 	fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1));
444 
445 #if FPE_DEBUG
446 	printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", fe->fe_f2.fp_exp,
447 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
448 #endif
449 
450 	/* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
451 	d = fpu_add(fe);
452 	CPYFPN(&fe->fe_f1, d);
453 	CPYFPN(&fe->fe_f2, &X);
454 	/* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
455 	d = fpu_add(fe);
456 
457 #if FPE_DEBUG
458 	printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n",
459 	       d->fp_sign ? '-' : '+', d->fp_exp,
460 	       d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]);
461 #endif
462 
463 	CPYFPN(&fe->fe_f1, d);
464 	CPYFPN(&fe->fe_f2, &KLOG2);
465 	/* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
466 	d = fpu_add(fe);
467     }
468 
469     return d;
470 }
471 
472 struct fpn *
473 fpu_log10(fe)
474      struct fpemu *fe;
475 {
476     struct fpn *fp = &fe->fe_f2;
477     u_int fpsr;
478 
479     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
480 
481     if (fp->fp_class >= FPC_NUM) {
482 	if (fp->fp_sign) {	/* negative number or Inf */
483 	    fp = fpu_newnan(fe);
484 	    fpsr |= FPSR_OPERR;
485 	} else if (fp->fp_class == FPC_NUM) {
486 	    /* the real work here */
487 	    fp = __fpu_logn(fe);
488 	    if (fp != &fe->fe_f1)
489 		CPYFPN(&fe->fe_f1, fp);
490 	    (void)fpu_const(&fe->fe_f2, 0x31 /* ln(10) */);
491 	    fp = fpu_div(fe);
492 	} /* else if fp == +Inf, return +Inf */
493     } else if (fp->fp_class == FPC_ZERO) {
494 	/* return -Inf */
495 	fp->fp_class = FPC_INF;
496 	fp->fp_sign = 1;
497 	fpsr |= FPSR_DZ;
498     } else if (fp->fp_class == FPC_SNAN) {
499 	fpsr |= FPSR_SNAN;
500 	fp = fpu_newnan(fe);
501     } else {
502 	fp = fpu_newnan(fe);
503     }
504 
505     fe->fe_fpsr = fpsr;
506 
507     return fp;
508 }
509 
510 struct fpn *
511 fpu_log2(fe)
512      struct fpemu *fe;
513 {
514     struct fpn *fp = &fe->fe_f2;
515     u_int fpsr;
516 
517     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
518 
519     if (fp->fp_class >= FPC_NUM) {
520 	if (fp->fp_sign) {	/* negative number or Inf */
521 	    fp = fpu_newnan(fe);
522 	    fpsr |= FPSR_OPERR;
523 	} else if (fp->fp_class == FPC_NUM) {
524 	    /* the real work here */
525 	    if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 &&
526 		fp->fp_mant[2] == 0) {
527 		/* fp == 2.0 ^ exp <--> log2(fp) == exp */
528 		fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, &fp->fp_exp);
529 		fp = &fe->fe_f3;
530 	    } else {
531 		fp = __fpu_logn(fe);
532 		if (fp != &fe->fe_f1)
533 		    CPYFPN(&fe->fe_f1, fp);
534 		(void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
535 		fp = fpu_div(fe);
536 	    }
537 	} /* else if fp == +Inf, return +Inf */
538     } else if (fp->fp_class == FPC_ZERO) {
539 	/* return -Inf */
540 	fp->fp_class = FPC_INF;
541 	fp->fp_sign = 1;
542 	fpsr |= FPSR_DZ;
543     } else if (fp->fp_class == FPC_SNAN) {
544 	fpsr |= FPSR_SNAN;
545 	fp = fpu_newnan(fe);
546     } else {
547 	fp = fpu_newnan(fe);
548     }
549 
550     fe->fe_fpsr = fpsr;
551     return fp;
552 }
553 
554 struct fpn *
555 fpu_logn(fe)
556      struct fpemu *fe;
557 {
558     struct fpn *fp = &fe->fe_f2;
559     u_int fpsr;
560 
561     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
562 
563     if (fp->fp_class >= FPC_NUM) {
564 	if (fp->fp_sign) {	/* negative number or Inf */
565 	    fp = fpu_newnan(fe);
566 	    fpsr |= FPSR_OPERR;
567 	} else if (fp->fp_class == FPC_NUM) {
568 	    /* the real work here */
569 	    fp = __fpu_logn(fe);
570 	} /* else if fp == +Inf, return +Inf */
571     } else if (fp->fp_class == FPC_ZERO) {
572 	/* return -Inf */
573 	fp->fp_class = FPC_INF;
574 	fp->fp_sign = 1;
575 	fpsr |= FPSR_DZ;
576     } else if (fp->fp_class == FPC_SNAN) {
577 	fpsr |= FPSR_SNAN;
578 	fp = fpu_newnan(fe);
579     } else {
580 	fp = fpu_newnan(fe);
581     }
582 
583     fe->fe_fpsr = fpsr;
584 
585     return fp;
586 }
587 
588 struct fpn *
589 fpu_lognp1(fe)
590      struct fpemu *fe;
591 {
592     struct fpn *fp;
593 
594     /* build a 1.0 */
595     fp = fpu_const(&fe->fe_f1, 0x32); /* get 1.0 */
596     /* fp = 1.0 + f2 */
597     fp = fpu_add(fe);
598 
599     /* copy the result to the src opr */
600     if (&fe->fe_f2 != fp)
601 	CPYFPN(&fe->fe_f2, fp);
602 
603     return fpu_logn(fe);
604 }
605