xref: /netbsd-src/sys/arch/m68k/fpe/fpu_log.c (revision 3cec974c61d7fac0a37c0377723a33214a458c8b)
1 /*	$NetBSD: fpu_log.c,v 1.7 2000/09/22 19:47:59 is 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/types.h>
35 #include <sys/systm.h>
36 
37 #include "fpu_emulate.h"
38 
39 static u_int logA6[] = { 0x3FC2499A, 0xB5E4040B };
40 static u_int logA5[] = { 0xBFC555B5, 0x848CB7DB };
41 static u_int logA4[] = { 0x3FC99999, 0x987D8730 };
42 static u_int logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 };
43 static u_int logA2[] = { 0x3FD55555, 0x555555A4 };
44 static u_int logA1[] = { 0xBFE00000, 0x00000008 };
45 
46 static u_int logB5[] = { 0x3F175496, 0xADD7DAD6 };
47 static u_int logB4[] = { 0x3F3C71C2, 0xFE80C7E0 };
48 static u_int logB3[] = { 0x3F624924, 0x928BCCFF };
49 static u_int logB2[] = { 0x3F899999, 0x999995EC };
50 static u_int logB1[] = { 0x3FB55555, 0x55555555 };
51 
52 /* sfpn = shortened fp number; can represent only positive numbers */
53 static struct sfpn {
54     int		sp_exp;
55     u_int	sp_m0, sp_m1;
56 } logtbl[] = {
57     { 0x3FFE - 0x3fff, 0xFE03F80FU, 0xE03F80FEU },
58     { 0x3FF7 - 0x3fff, 0xFF015358U, 0x833C47E2U },
59     { 0x3FFE - 0x3fff, 0xFA232CF2U, 0x52138AC0U },
60     { 0x3FF9 - 0x3fff, 0xBDC8D83EU, 0xAD88D549U },
61     { 0x3FFE - 0x3fff, 0xF6603D98U, 0x0F6603DAU },
62     { 0x3FFA - 0x3fff, 0x9CF43DCFU, 0xF5EAFD48U },
63     { 0x3FFE - 0x3fff, 0xF2B9D648U, 0x0F2B9D65U },
64     { 0x3FFA - 0x3fff, 0xDA16EB88U, 0xCB8DF614U },
65     { 0x3FFE - 0x3fff, 0xEF2EB71FU, 0xC4345238U },
66     { 0x3FFB - 0x3fff, 0x8B29B775U, 0x1BD70743U },
67     { 0x3FFE - 0x3fff, 0xEBBDB2A5U, 0xC1619C8CU },
68     { 0x3FFB - 0x3fff, 0xA8D839F8U, 0x30C1FB49U },
69     { 0x3FFE - 0x3fff, 0xE865AC7BU, 0x7603A197U },
70     { 0x3FFB - 0x3fff, 0xC61A2EB1U, 0x8CD907ADU },
71     { 0x3FFE - 0x3fff, 0xE525982AU, 0xF70C880EU },
72     { 0x3FFB - 0x3fff, 0xE2F2A47AU, 0xDE3A18AFU },
73     { 0x3FFE - 0x3fff, 0xE1FC780EU, 0x1FC780E2U },
74     { 0x3FFB - 0x3fff, 0xFF64898EU, 0xDF55D551U },
75     { 0x3FFE - 0x3fff, 0xDEE95C4CU, 0xA037BA57U },
76     { 0x3FFC - 0x3fff, 0x8DB956A9U, 0x7B3D0148U },
77     { 0x3FFE - 0x3fff, 0xDBEB61EEU, 0xD19C5958U },
78     { 0x3FFC - 0x3fff, 0x9B8FE100U, 0xF47BA1DEU },
79     { 0x3FFE - 0x3fff, 0xD901B203U, 0x6406C80EU },
80     { 0x3FFC - 0x3fff, 0xA9372F1DU, 0x0DA1BD17U },
81     { 0x3FFE - 0x3fff, 0xD62B80D6U, 0x2B80D62CU },
82     { 0x3FFC - 0x3fff, 0xB6B07F38U, 0xCE90E46BU },
83     { 0x3FFE - 0x3fff, 0xD3680D36U, 0x80D3680DU },
84     { 0x3FFC - 0x3fff, 0xC3FD0329U, 0x06488481U },
85     { 0x3FFE - 0x3fff, 0xD0B69FCBU, 0xD2580D0BU },
86     { 0x3FFC - 0x3fff, 0xD11DE0FFU, 0x15AB18CAU },
87     { 0x3FFE - 0x3fff, 0xCE168A77U, 0x25080CE1U },
88     { 0x3FFC - 0x3fff, 0xDE1433A1U, 0x6C66B150U },
89     { 0x3FFE - 0x3fff, 0xCB8727C0U, 0x65C393E0U },
90     { 0x3FFC - 0x3fff, 0xEAE10B5AU, 0x7DDC8ADDU },
91     { 0x3FFE - 0x3fff, 0xC907DA4EU, 0x871146ADU },
92     { 0x3FFC - 0x3fff, 0xF7856E5EU, 0xE2C9B291U },
93     { 0x3FFE - 0x3fff, 0xC6980C69U, 0x80C6980CU },
94     { 0x3FFD - 0x3fff, 0x82012CA5U, 0xA68206D7U },
95     { 0x3FFE - 0x3fff, 0xC4372F85U, 0x5D824CA6U },
96     { 0x3FFD - 0x3fff, 0x882C5FCDU, 0x7256A8C5U },
97     { 0x3FFE - 0x3fff, 0xC1E4BBD5U, 0x95F6E947U },
98     { 0x3FFD - 0x3fff, 0x8E44C60BU, 0x4CCFD7DEU },
99     { 0x3FFE - 0x3fff, 0xBFA02FE8U, 0x0BFA02FFU },
100     { 0x3FFD - 0x3fff, 0x944AD09EU, 0xF4351AF6U },
101     { 0x3FFE - 0x3fff, 0xBD691047U, 0x07661AA3U },
102     { 0x3FFD - 0x3fff, 0x9A3EECD4U, 0xC3EAA6B2U },
103     { 0x3FFE - 0x3fff, 0xBB3EE721U, 0xA54D880CU },
104     { 0x3FFD - 0x3fff, 0xA0218434U, 0x353F1DE8U },
105     { 0x3FFE - 0x3fff, 0xB92143FAU, 0x36F5E02EU },
106     { 0x3FFD - 0x3fff, 0xA5F2FCABU, 0xBBC506DAU },
107     { 0x3FFE - 0x3fff, 0xB70FBB5AU, 0x19BE3659U },
108     { 0x3FFD - 0x3fff, 0xABB3B8BAU, 0x2AD362A5U },
109     { 0x3FFE - 0x3fff, 0xB509E68AU, 0x9B94821FU },
110     { 0x3FFD - 0x3fff, 0xB1641795U, 0xCE3CA97BU },
111     { 0x3FFE - 0x3fff, 0xB30F6352U, 0x8917C80BU },
112     { 0x3FFD - 0x3fff, 0xB7047551U, 0x5D0F1C61U },
113     { 0x3FFE - 0x3fff, 0xB11FD3B8U, 0x0B11FD3CU },
114     { 0x3FFD - 0x3fff, 0xBC952AFEU, 0xEA3D13E1U },
115     { 0x3FFE - 0x3fff, 0xAF3ADDC6U, 0x80AF3ADEU },
116     { 0x3FFD - 0x3fff, 0xC2168ED0U, 0xF458BA4AU },
117     { 0x3FFE - 0x3fff, 0xAD602B58U, 0x0AD602B6U },
118     { 0x3FFD - 0x3fff, 0xC788F439U, 0xB3163BF1U },
119     { 0x3FFE - 0x3fff, 0xAB8F69E2U, 0x8359CD11U },
120     { 0x3FFD - 0x3fff, 0xCCECAC08U, 0xBF04565DU },
121     { 0x3FFE - 0x3fff, 0xA9C84A47U, 0xA07F5638U },
122     { 0x3FFD - 0x3fff, 0xD2420487U, 0x2DD85160U },
123     { 0x3FFE - 0x3fff, 0xA80A80A8U, 0x0A80A80BU },
124     { 0x3FFD - 0x3fff, 0xD7894992U, 0x3BC3588AU },
125     { 0x3FFE - 0x3fff, 0xA655C439U, 0x2D7B73A8U },
126     { 0x3FFD - 0x3fff, 0xDCC2C4B4U, 0x9887DACCU },
127     { 0x3FFE - 0x3fff, 0xA4A9CF1DU, 0x96833751U },
128     { 0x3FFD - 0x3fff, 0xE1EEBD3EU, 0x6D6A6B9EU },
129     { 0x3FFE - 0x3fff, 0xA3065E3FU, 0xAE7CD0E0U },
130     { 0x3FFD - 0x3fff, 0xE70D785CU, 0x2F9F5BDCU },
131     { 0x3FFE - 0x3fff, 0xA16B312EU, 0xA8FC377DU },
132     { 0x3FFD - 0x3fff, 0xEC1F392CU, 0x5179F283U },
133     { 0x3FFE - 0x3fff, 0x9FD809FDU, 0x809FD80AU },
134     { 0x3FFD - 0x3fff, 0xF12440D3U, 0xE36130E6U },
135     { 0x3FFE - 0x3fff, 0x9E4CAD23U, 0xDD5F3A20U },
136     { 0x3FFD - 0x3fff, 0xF61CCE92U, 0x346600BBU },
137     { 0x3FFE - 0x3fff, 0x9CC8E160U, 0xC3FB19B9U },
138     { 0x3FFD - 0x3fff, 0xFB091FD3U, 0x8145630AU },
139     { 0x3FFE - 0x3fff, 0x9B4C6F9EU, 0xF03A3CAAU },
140     { 0x3FFD - 0x3fff, 0xFFE97042U, 0xBFA4C2ADU },
141     { 0x3FFE - 0x3fff, 0x99D722DAU, 0xBDE58F06U },
142     { 0x3FFE - 0x3fff, 0x825EFCEDU, 0x49369330U },
143     { 0x3FFE - 0x3fff, 0x9868C809U, 0x868C8098U },
144     { 0x3FFE - 0x3fff, 0x84C37A7AU, 0xB9A905C9U },
145     { 0x3FFE - 0x3fff, 0x97012E02U, 0x5C04B809U },
146     { 0x3FFE - 0x3fff, 0x87224C2EU, 0x8E645FB7U },
147     { 0x3FFE - 0x3fff, 0x95A02568U, 0x095A0257U },
148     { 0x3FFE - 0x3fff, 0x897B8CACU, 0x9F7DE298U },
149     { 0x3FFE - 0x3fff, 0x94458094U, 0x45809446U },
150     { 0x3FFE - 0x3fff, 0x8BCF55DEU, 0xC4CD05FEU },
151     { 0x3FFE - 0x3fff, 0x92F11384U, 0x0497889CU },
152     { 0x3FFE - 0x3fff, 0x8E1DC0FBU, 0x89E125E5U },
153     { 0x3FFE - 0x3fff, 0x91A2B3C4U, 0xD5E6F809U },
154     { 0x3FFE - 0x3fff, 0x9066E68CU, 0x955B6C9BU },
155     { 0x3FFE - 0x3fff, 0x905A3863U, 0x3E06C43BU },
156     { 0x3FFE - 0x3fff, 0x92AADE74U, 0xC7BE59E0U },
157     { 0x3FFE - 0x3fff, 0x8F1779D9U, 0xFDC3A219U },
158     { 0x3FFE - 0x3fff, 0x94E9BFF6U, 0x15845643U },
159     { 0x3FFE - 0x3fff, 0x8DDA5202U, 0x37694809U },
160     { 0x3FFE - 0x3fff, 0x9723A1B7U, 0x20134203U },
161     { 0x3FFE - 0x3fff, 0x8CA29C04U, 0x6514E023U },
162     { 0x3FFE - 0x3fff, 0x995899C8U, 0x90EB8990U },
163     { 0x3FFE - 0x3fff, 0x8B70344AU, 0x139BC75AU },
164     { 0x3FFE - 0x3fff, 0x9B88BDAAU, 0x3A3DAE2FU },
165     { 0x3FFE - 0x3fff, 0x8A42F870U, 0x5669DB46U },
166     { 0x3FFE - 0x3fff, 0x9DB4224FU, 0xFFE1157CU },
167     { 0x3FFE - 0x3fff, 0x891AC73AU, 0xE9819B50U },
168     { 0x3FFE - 0x3fff, 0x9FDADC26U, 0x8B7A12DAU },
169     { 0x3FFE - 0x3fff, 0x87F78087U, 0xF78087F8U },
170     { 0x3FFE - 0x3fff, 0xA1FCFF17U, 0xCE733BD4U },
171     { 0x3FFE - 0x3fff, 0x86D90544U, 0x7A34ACC6U },
172     { 0x3FFE - 0x3fff, 0xA41A9E8FU, 0x5446FB9FU },
173     { 0x3FFE - 0x3fff, 0x85BF3761U, 0x2CEE3C9BU },
174     { 0x3FFE - 0x3fff, 0xA633CD7EU, 0x6771CD8BU },
175     { 0x3FFE - 0x3fff, 0x84A9F9C8U, 0x084A9F9DU },
176     { 0x3FFE - 0x3fff, 0xA8489E60U, 0x0B435A5EU },
177     { 0x3FFE - 0x3fff, 0x83993052U, 0x3FBE3368U },
178     { 0x3FFE - 0x3fff, 0xAA59233CU, 0xCCA4BD49U },
179     { 0x3FFE - 0x3fff, 0x828CBFBEU, 0xB9A020A3U },
180     { 0x3FFE - 0x3fff, 0xAC656DAEU, 0x6BCC4985U },
181     { 0x3FFE - 0x3fff, 0x81848DA8U, 0xFAF0D277U },
182     { 0x3FFE - 0x3fff, 0xAE6D8EE3U, 0x60BB2468U },
183     { 0x3FFE - 0x3fff, 0x80808080U, 0x80808081U },
184     { 0x3FFE - 0x3fff, 0xB07197A2U, 0x3C46C654U },
185 };
186 
187 static struct fpn *__fpu_logn __P((struct fpemu *fe));
188 
189 /*
190  * natural log - algorithm taken from Motorola FPSP,
191  * except this doesn't bother to check for invalid input.
192  */
193 static struct fpn *
194 __fpu_logn(fe)
195      struct fpemu *fe;
196 {
197     static struct fpn X, F, U, V, W, KLOG2;
198     struct fpn *d;
199     int i, k;
200 
201     CPYFPN(&X, &fe->fe_f2);
202 
203     /* see if |X-1| < 1/16 approx. */
204     if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) ||
205 	(0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) {
206 	/* log near 1 */
207 #if FPE_DEBUG
208 	printf("__fpu_logn: log near 1\n");
209 #endif
210 
211 	fpu_const(&fe->fe_f1, 0x32);
212 	/* X+1 */
213 	d = fpu_add(fe);
214 	CPYFPN(&V, d);
215 
216 	CPYFPN(&fe->fe_f1, &X);
217 	fpu_const(&fe->fe_f2, 0x32); /* 1.0 */
218 	fe->fe_f2.fp_sign = 1; /* -1.0 */
219 	/* X-1 */
220 	d = fpu_add(fe);
221 	CPYFPN(&fe->fe_f1, d);
222 	/* 2(X-1) */
223 	fe->fe_f1.fp_exp++; /* *= 2 */
224 	CPYFPN(&fe->fe_f2, &V);
225 	/* U=2(X-1)/(X+1) */
226 	d = fpu_div(fe);
227 	CPYFPN(&U, d);
228 	CPYFPN(&fe->fe_f1, d);
229 	CPYFPN(&fe->fe_f2, d);
230 	/* V=U*U */
231 	d = fpu_mul(fe);
232 	CPYFPN(&V, d);
233 	CPYFPN(&fe->fe_f1, d);
234 	CPYFPN(&fe->fe_f2, d);
235 	/* W=V*V */
236 	d = fpu_mul(fe);
237 	CPYFPN(&W, d);
238 
239 	/* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */
240 
241 	/* B1+W*(B3+W*B5) part */
242 	CPYFPN(&fe->fe_f1, d);
243 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5);
244 	/* W*B5 */
245 	d = fpu_mul(fe);
246 	CPYFPN(&fe->fe_f1, d);
247 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3);
248 	/* B3+W*B5 */
249 	d = fpu_add(fe);
250 	CPYFPN(&fe->fe_f1, d);
251 	CPYFPN(&fe->fe_f2, &W);
252 	/* W*(B3+W*B5) */
253 	d = fpu_mul(fe);
254 	CPYFPN(&fe->fe_f1, d);
255 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1);
256 	/* B1+W*(B3+W*B5) */
257 	d = fpu_add(fe);
258 	CPYFPN(&X, d);
259 
260 	/* [V*(B2+W*B4)] part */
261 	CPYFPN(&fe->fe_f1, &W);
262 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4);
263 	/* W*B4 */
264 	d = fpu_mul(fe);
265 	CPYFPN(&fe->fe_f1, d);
266 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2);
267 	/* B2+W*B4 */
268 	d = fpu_add(fe);
269 	CPYFPN(&fe->fe_f1, d);
270 	CPYFPN(&fe->fe_f2, &V);
271 	/* V*(B2+W*B4) */
272 	d = fpu_mul(fe);
273 	CPYFPN(&fe->fe_f1, d);
274 	CPYFPN(&fe->fe_f2, &X);
275 	/* B1+W*(B3+W*B5)+V*(B2+W*B4) */
276 	d = fpu_add(fe);
277 	CPYFPN(&fe->fe_f1, d);
278 	CPYFPN(&fe->fe_f2, &V);
279 	/* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
280 	d = fpu_mul(fe);
281 	CPYFPN(&fe->fe_f1, d);
282 	CPYFPN(&fe->fe_f2, &U);
283 	/* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
284 	d = fpu_mul(fe);
285 	CPYFPN(&fe->fe_f1, d);
286 	CPYFPN(&fe->fe_f2, &U);
287 	/* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
288 	d = fpu_add(fe);
289     } else /* the usual case */ {
290 #if FPE_DEBUG
291 	printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n",
292 	       X.fp_exp, X.fp_mant[0], X.fp_mant[1]);
293 #endif
294 
295 	k = X.fp_exp;
296 	/* X <- Y */
297 	X.fp_exp = fe->fe_f2.fp_exp = 0;
298 
299 	/* get the most significant 7 bits of X */
300 	F.fp_class = FPC_NUM;
301 	F.fp_sign = 0;
302 	F.fp_exp = X.fp_exp;
303 	F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG));
304 	F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG));
305 	F.fp_mant[1] = F.fp_mant[2] = 0;
306 	F.fp_sticky = 0;
307 
308 #if FPE_DEBUG
309 	printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n",
310 	       fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0],
311 	       fe->fe_f2.fp_mant[1], k);
312 	printf("__fpu_logn: F=(%d,%08x,%08x...)\n",
313 	       F.fp_exp, F.fp_mant[0], F.fp_mant[1]);
314 #endif
315 
316 	/* index to the table */
317 	i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e;
318 
319 #if FPE_DEBUG
320 	printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i);
321 #endif
322 
323 	CPYFPN(&fe->fe_f1, &F);
324 	/* -F */
325 	fe->fe_f1.fp_sign = 1;
326 	/* Y-F */
327 	d = fpu_add(fe);
328 	CPYFPN(&fe->fe_f1, d);
329 
330 	/* fe_f2 = 1/F */
331 	fe->fe_f2.fp_class = FPC_NUM;
332 	fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
333 	fe->fe_f2.fp_exp = logtbl[i].sp_exp;
334 	fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
335 	fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
336 	    (logtbl[i].sp_m1 >> (31 - FP_LG));
337 	fe->fe_f2.fp_mant[2] = (u_int)(logtbl[i].sp_m1 << (FP_LG + 1));
338 
339 #if FPE_DEBUG
340 	printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
341 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
342 #endif
343 
344 	/* U = (Y-F) * (1/F) */
345 	d = fpu_mul(fe);
346 	CPYFPN(&U, d);
347 
348 	/* KLOG2 = K * ln(2) */
349 	/* fe_f1 == (fpn)k */
350 	fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k);
351 	(void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
352 #if FPE_DEBUG
353 	printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", fe->fe_f1.fp_exp,
354 	       fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]);
355 	printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
356 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
357 #endif
358 	/* K * LOGOF2 */
359 	d = fpu_mul(fe);
360 	CPYFPN(&KLOG2, d);
361 
362 	/* V=U*U */
363 	CPYFPN(&fe->fe_f1, &U);
364 	CPYFPN(&fe->fe_f2, &U);
365 	d = fpu_mul(fe);
366 	CPYFPN(&V, d);
367 
368 	/*
369 	 * approximation of LOG(1+U) by
370 	 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6)))
371 	 */
372 
373 	/* (U+V*(A1+V*(A3+V*A5))) part */
374 	CPYFPN(&fe->fe_f1, d);
375 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5);
376 	/* V*A5 */
377 	d = fpu_mul(fe);
378 
379 	CPYFPN(&fe->fe_f1, d);
380 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3);
381 	/* A3+V*A5 */
382 	d = fpu_add(fe);
383 
384 	CPYFPN(&fe->fe_f1, d);
385 	CPYFPN(&fe->fe_f2, &V);
386 	/* V*(A3+V*A5) */
387 	d = fpu_mul(fe);
388 
389 	CPYFPN(&fe->fe_f1, d);
390 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1);
391 	/* A1+V*(A3+V*A5) */
392 	d = fpu_add(fe);
393 
394 	CPYFPN(&fe->fe_f1, d);
395 	CPYFPN(&fe->fe_f2, &V);
396 	/* V*(A1+V*(A3+V*A5)) */
397 	d = fpu_mul(fe);
398 
399 	CPYFPN(&fe->fe_f1, d);
400 	CPYFPN(&fe->fe_f2, &U);
401 	/* U+V*(A1+V*(A3+V*A5)) */
402 	d = fpu_add(fe);
403 
404 	CPYFPN(&X, d);
405 
406 	/* (U*V*(A2+V*(A4+V*A6))) part */
407 	CPYFPN(&fe->fe_f1, &V);
408 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6);
409 	/* V*A6 */
410 	d = fpu_mul(fe);
411 	CPYFPN(&fe->fe_f1, d);
412 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4);
413 	/* A4+V*A6 */
414 	d = fpu_add(fe);
415 	CPYFPN(&fe->fe_f1, d);
416 	CPYFPN(&fe->fe_f2, &V);
417 	/* V*(A4+V*A6) */
418 	d = fpu_mul(fe);
419 	CPYFPN(&fe->fe_f1, d);
420 	fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2);
421 	/* A2+V*(A4+V*A6) */
422 	d = fpu_add(fe);
423 	CPYFPN(&fe->fe_f1, d);
424 	CPYFPN(&fe->fe_f2, &V);
425 	/* V*(A2+V*(A4+V*A6)) */
426 	d = fpu_mul(fe);
427 	CPYFPN(&fe->fe_f1, d);
428 	CPYFPN(&fe->fe_f2, &U);
429 	/* U*V*(A2+V*(A4+V*A6)) */
430 	d = fpu_mul(fe);
431 	CPYFPN(&fe->fe_f1, d);
432 	i++;
433 	/* fe_f2 = logtbl[i+1] (== LOG(F)) */
434 	fe->fe_f2.fp_class = FPC_NUM;
435 	fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
436 	fe->fe_f2.fp_exp = logtbl[i].sp_exp;
437 	fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
438 	fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
439 	    (logtbl[i].sp_m1 >> (31 - FP_LG));
440 	fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1));
441 
442 #if FPE_DEBUG
443 	printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", fe->fe_f2.fp_exp,
444 	       fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
445 #endif
446 
447 	/* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
448 	d = fpu_add(fe);
449 	CPYFPN(&fe->fe_f1, d);
450 	CPYFPN(&fe->fe_f2, &X);
451 	/* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
452 	d = fpu_add(fe);
453 
454 #if FPE_DEBUG
455 	printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n",
456 	       d->fp_sign ? '-' : '+', d->fp_exp,
457 	       d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]);
458 #endif
459 
460 	CPYFPN(&fe->fe_f1, d);
461 	CPYFPN(&fe->fe_f2, &KLOG2);
462 	/* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
463 	d = fpu_add(fe);
464     }
465 
466     return d;
467 }
468 
469 struct fpn *
470 fpu_log10(fe)
471      struct fpemu *fe;
472 {
473     struct fpn *fp = &fe->fe_f2;
474     u_int fpsr;
475 
476     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
477 
478     if (fp->fp_class >= FPC_NUM) {
479 	if (fp->fp_sign) {	/* negative number or Inf */
480 	    fp = fpu_newnan(fe);
481 	    fpsr |= FPSR_OPERR;
482 	} else if (fp->fp_class == FPC_NUM) {
483 	    /* the real work here */
484 	    fp = __fpu_logn(fe);
485 	    if (fp != &fe->fe_f1)
486 		CPYFPN(&fe->fe_f1, fp);
487 	    (void)fpu_const(&fe->fe_f2, 0x31 /* ln(10) */);
488 	    fp = fpu_div(fe);
489 	} /* else if fp == +Inf, return +Inf */
490     } else if (fp->fp_class == FPC_ZERO) {
491 	/* return -Inf */
492 	fp->fp_class = FPC_INF;
493 	fp->fp_sign = 1;
494 	fpsr |= FPSR_DZ;
495     } else if (fp->fp_class == FPC_SNAN) {
496 	fpsr |= FPSR_SNAN;
497 	fp = fpu_newnan(fe);
498     } else {
499 	fp = fpu_newnan(fe);
500     }
501 
502     fe->fe_fpsr = fpsr;
503 
504     return fp;
505 }
506 
507 struct fpn *
508 fpu_log2(fe)
509      struct fpemu *fe;
510 {
511     struct fpn *fp = &fe->fe_f2;
512     u_int fpsr;
513 
514     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
515 
516     if (fp->fp_class >= FPC_NUM) {
517 	if (fp->fp_sign) {	/* negative number or Inf */
518 	    fp = fpu_newnan(fe);
519 	    fpsr |= FPSR_OPERR;
520 	} else if (fp->fp_class == FPC_NUM) {
521 	    /* the real work here */
522 	    if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 &&
523 		fp->fp_mant[2] == 0) {
524 		/* fp == 2.0 ^ exp <--> log2(fp) == exp */
525 		fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, &fp->fp_exp);
526 		fp = &fe->fe_f3;
527 	    } else {
528 		fp = __fpu_logn(fe);
529 		if (fp != &fe->fe_f1)
530 		    CPYFPN(&fe->fe_f1, fp);
531 		(void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
532 		fp = fpu_div(fe);
533 	    }
534 	} /* else if fp == +Inf, return +Inf */
535     } else if (fp->fp_class == FPC_ZERO) {
536 	/* return -Inf */
537 	fp->fp_class = FPC_INF;
538 	fp->fp_sign = 1;
539 	fpsr |= FPSR_DZ;
540     } else if (fp->fp_class == FPC_SNAN) {
541 	fpsr |= FPSR_SNAN;
542 	fp = fpu_newnan(fe);
543     } else {
544 	fp = fpu_newnan(fe);
545     }
546 
547     fe->fe_fpsr = fpsr;
548     return fp;
549 }
550 
551 struct fpn *
552 fpu_logn(fe)
553      struct fpemu *fe;
554 {
555     struct fpn *fp = &fe->fe_f2;
556     u_int fpsr;
557 
558     fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
559 
560     if (fp->fp_class >= FPC_NUM) {
561 	if (fp->fp_sign) {	/* negative number or Inf */
562 	    fp = fpu_newnan(fe);
563 	    fpsr |= FPSR_OPERR;
564 	} else if (fp->fp_class == FPC_NUM) {
565 	    /* the real work here */
566 	    fp = __fpu_logn(fe);
567 	} /* else if fp == +Inf, return +Inf */
568     } else if (fp->fp_class == FPC_ZERO) {
569 	/* return -Inf */
570 	fp->fp_class = FPC_INF;
571 	fp->fp_sign = 1;
572 	fpsr |= FPSR_DZ;
573     } else if (fp->fp_class == FPC_SNAN) {
574 	fpsr |= FPSR_SNAN;
575 	fp = fpu_newnan(fe);
576     } else {
577 	fp = fpu_newnan(fe);
578     }
579 
580     fe->fe_fpsr = fpsr;
581 
582     return fp;
583 }
584 
585 struct fpn *
586 fpu_lognp1(fe)
587      struct fpemu *fe;
588 {
589     struct fpn *fp;
590 
591     /* build a 1.0 */
592     fp = fpu_const(&fe->fe_f1, 0x32); /* get 1.0 */
593     /* fp = 1.0 + f2 */
594     fp = fpu_add(fe);
595 
596     /* copy the result to the src opr */
597     if (&fe->fe_f2 != fp)
598 	CPYFPN(&fe->fe_f2, fp);
599 
600     return fpu_logn(fe);
601 }
602