1/*	$NetBSD: fpu_log.c,v 1.17 2013/04/20 05:27:05 isaki 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 1.17 2013/04/20 05:27:05 isaki Exp $");
36
37#include <sys/types.h>
38#include <sys/systm.h>
39
40#include "fpu_emulate.h"
41
42static uint32_t logA6[] = { 0x3FC2499A, 0xB5E4040B };
43static uint32_t logA5[] = { 0xBFC555B5, 0x848CB7DB };
44static uint32_t logA4[] = { 0x3FC99999, 0x987D8730 };
45static uint32_t logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 };
46static uint32_t logA2[] = { 0x3FD55555, 0x555555A4 };
47static uint32_t logA1[] = { 0xBFE00000, 0x00000008 };
48
49static uint32_t logB5[] = { 0x3F175496, 0xADD7DAD6 };
50static uint32_t logB4[] = { 0x3F3C71C2, 0xFE80C7E0 };
51static uint32_t logB3[] = { 0x3F624924, 0x928BCCFF };
52static uint32_t logB2[] = { 0x3F899999, 0x999995EC };
53static uint32_t logB1[] = { 0x3FB55555, 0x55555555 };
54
55/* sfpn = shortened fp number; can represent only positive numbers */
56static struct sfpn {
57	int		sp_exp;
58	uint32_t	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
190static struct fpn *__fpu_logn(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 */
196static struct fpn *
197__fpu_logn(struct fpemu *fe)
198{
199	static struct fpn X, F, U, V, W, KLOG2;
200	struct fpn *d;
201	int i, k;
202
203	CPYFPN(&X, &fe->fe_f2);
204
205	/* see if |X-1| < 1/16 approx. */
206	if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) ||
207	    (0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) {
208		/* log near 1 */
209#if FPE_DEBUG
210		printf("__fpu_logn: log near 1\n");
211#endif
212
213		fpu_const(&fe->fe_f1, FPU_CONST_1);
214		/* X+1 */
215		d = fpu_add(fe);
216		CPYFPN(&V, d);
217
218		CPYFPN(&fe->fe_f1, &X);
219		fpu_const(&fe->fe_f2, FPU_CONST_1);
220		fe->fe_f2.fp_sign = 1; /* -1.0 */
221		/* X-1 */
222		d = fpu_add(fe);
223		CPYFPN(&fe->fe_f1, d);
224		/* 2(X-1) */
225		fe->fe_f1.fp_exp++; /* *= 2 */
226		CPYFPN(&fe->fe_f2, &V);
227		/* U=2(X-1)/(X+1) */
228		d = fpu_div(fe);
229		CPYFPN(&U, d);
230		CPYFPN(&fe->fe_f1, d);
231		CPYFPN(&fe->fe_f2, d);
232		/* V=U*U */
233		d = fpu_mul(fe);
234		CPYFPN(&V, d);
235		CPYFPN(&fe->fe_f1, d);
236		CPYFPN(&fe->fe_f2, d);
237		/* W=V*V */
238		d = fpu_mul(fe);
239		CPYFPN(&W, d);
240
241		/* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */
242
243		/* B1+W*(B3+W*B5) part */
244		CPYFPN(&fe->fe_f1, d);
245		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5);
246		/* W*B5 */
247		d = fpu_mul(fe);
248		CPYFPN(&fe->fe_f1, d);
249		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3);
250		/* B3+W*B5 */
251		d = fpu_add(fe);
252		CPYFPN(&fe->fe_f1, d);
253		CPYFPN(&fe->fe_f2, &W);
254		/* W*(B3+W*B5) */
255		d = fpu_mul(fe);
256		CPYFPN(&fe->fe_f1, d);
257		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1);
258		/* B1+W*(B3+W*B5) */
259		d = fpu_add(fe);
260		CPYFPN(&X, d);
261
262		/* [V*(B2+W*B4)] part */
263		CPYFPN(&fe->fe_f1, &W);
264		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4);
265		/* W*B4 */
266		d = fpu_mul(fe);
267		CPYFPN(&fe->fe_f1, d);
268		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2);
269		/* B2+W*B4 */
270		d = fpu_add(fe);
271		CPYFPN(&fe->fe_f1, d);
272		CPYFPN(&fe->fe_f2, &V);
273		/* V*(B2+W*B4) */
274		d = fpu_mul(fe);
275		CPYFPN(&fe->fe_f1, d);
276		CPYFPN(&fe->fe_f2, &X);
277		/* B1+W*(B3+W*B5)+V*(B2+W*B4) */
278		d = fpu_add(fe);
279		CPYFPN(&fe->fe_f1, d);
280		CPYFPN(&fe->fe_f2, &V);
281		/* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
282		d = fpu_mul(fe);
283		CPYFPN(&fe->fe_f1, d);
284		CPYFPN(&fe->fe_f2, &U);
285		/* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
286		d = fpu_mul(fe);
287		CPYFPN(&fe->fe_f1, d);
288		CPYFPN(&fe->fe_f2, &U);
289		/* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
290		d = fpu_add(fe);
291	} else /* the usual case */ {
292#if FPE_DEBUG
293		printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n",
294		    X.fp_exp, X.fp_mant[0], X.fp_mant[1]);
295#endif
296
297		k = X.fp_exp;
298		/* X <- Y */
299		X.fp_exp = fe->fe_f2.fp_exp = 0;
300
301		/* get the most significant 7 bits of X */
302		F.fp_class = FPC_NUM;
303		F.fp_sign = 0;
304		F.fp_exp = X.fp_exp;
305		F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG));
306		F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG));
307		F.fp_mant[1] = F.fp_mant[2] = 0;
308		F.fp_sticky = 0;
309
310#if FPE_DEBUG
311		printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n",
312		    fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0],
313		    fe->fe_f2.fp_mant[1], k);
314		printf("__fpu_logn: F=(%d,%08x,%08x...)\n",
315		    F.fp_exp, F.fp_mant[0], F.fp_mant[1]);
316#endif
317
318		/* index to the table */
319		i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e;
320
321#if FPE_DEBUG
322		printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i);
323#endif
324
325		CPYFPN(&fe->fe_f1, &F);
326		/* -F */
327		fe->fe_f1.fp_sign = 1;
328		/* Y-F */
329		d = fpu_add(fe);
330		CPYFPN(&fe->fe_f1, d);
331
332		/* fe_f2 = 1/F */
333		fe->fe_f2.fp_class = FPC_NUM;
334		fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2]
335		    = 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] =
341			(uint32_t)(logtbl[i].sp_m1 << (FP_LG + 1));
342
343#if FPE_DEBUG
344		printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
345		    fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
346#endif
347
348		/* U = (Y-F) * (1/F) */
349		d = fpu_mul(fe);
350		CPYFPN(&U, d);
351
352		/* KLOG2 = K * ln(2) */
353		/* fe_f1 == (fpn)k */
354		fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k);
355		(void)fpu_const(&fe->fe_f2, FPU_CONST_LN_2);
356#if FPE_DEBUG
357		printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n",
358		    fe->fe_f1.fp_exp,
359		    fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]);
360		printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n",
361		    fe->fe_f2.fp_exp,
362		    fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
363#endif
364		/* K * LOGOF2 */
365		d = fpu_mul(fe);
366		CPYFPN(&KLOG2, d);
367
368		/* V=U*U */
369		CPYFPN(&fe->fe_f1, &U);
370		CPYFPN(&fe->fe_f2, &U);
371		d = fpu_mul(fe);
372		CPYFPN(&V, d);
373
374		/*
375		 * approximation of LOG(1+U) by
376		 * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6)))
377		 */
378
379		/* (U+V*(A1+V*(A3+V*A5))) part */
380		CPYFPN(&fe->fe_f1, d);
381		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5);
382		/* V*A5 */
383		d = fpu_mul(fe);
384
385		CPYFPN(&fe->fe_f1, d);
386		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3);
387		/* A3+V*A5 */
388		d = fpu_add(fe);
389
390		CPYFPN(&fe->fe_f1, d);
391		CPYFPN(&fe->fe_f2, &V);
392		/* V*(A3+V*A5) */
393		d = fpu_mul(fe);
394
395		CPYFPN(&fe->fe_f1, d);
396		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1);
397		/* A1+V*(A3+V*A5) */
398		d = fpu_add(fe);
399
400		CPYFPN(&fe->fe_f1, d);
401		CPYFPN(&fe->fe_f2, &V);
402		/* V*(A1+V*(A3+V*A5)) */
403		d = fpu_mul(fe);
404
405		CPYFPN(&fe->fe_f1, d);
406		CPYFPN(&fe->fe_f2, &U);
407		/* U+V*(A1+V*(A3+V*A5)) */
408		d = fpu_add(fe);
409
410		CPYFPN(&X, d);
411
412		/* (U*V*(A2+V*(A4+V*A6))) part */
413		CPYFPN(&fe->fe_f1, &V);
414		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6);
415		/* V*A6 */
416		d = fpu_mul(fe);
417		CPYFPN(&fe->fe_f1, d);
418		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4);
419		/* A4+V*A6 */
420		d = fpu_add(fe);
421		CPYFPN(&fe->fe_f1, d);
422		CPYFPN(&fe->fe_f2, &V);
423		/* V*(A4+V*A6) */
424		d = fpu_mul(fe);
425		CPYFPN(&fe->fe_f1, d);
426		fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2);
427		/* A2+V*(A4+V*A6) */
428		d = fpu_add(fe);
429		CPYFPN(&fe->fe_f1, d);
430		CPYFPN(&fe->fe_f2, &V);
431		/* V*(A2+V*(A4+V*A6)) */
432		d = fpu_mul(fe);
433		CPYFPN(&fe->fe_f1, d);
434		CPYFPN(&fe->fe_f2, &U);
435		/* U*V*(A2+V*(A4+V*A6)) */
436		d = fpu_mul(fe);
437		CPYFPN(&fe->fe_f1, d);
438		i++;
439		/* fe_f2 = logtbl[i+1] (== LOG(F)) */
440		fe->fe_f2.fp_class = FPC_NUM;
441		fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2]
442		    = 0;
443		fe->fe_f2.fp_exp = logtbl[i].sp_exp;
444		fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
445		fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
446		    (logtbl[i].sp_m1 >> (31 - FP_LG));
447		fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1));
448
449#if FPE_DEBUG
450		printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n",
451		    fe->fe_f2.fp_exp,
452		    fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
453#endif
454
455		/* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
456		d = fpu_add(fe);
457		CPYFPN(&fe->fe_f1, d);
458		CPYFPN(&fe->fe_f2, &X);
459		/* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
460		d = fpu_add(fe);
461
462#if FPE_DEBUG
463		printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n",
464		    d->fp_sign ? '-' : '+', d->fp_exp,
465		    d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]);
466#endif
467
468		CPYFPN(&fe->fe_f1, d);
469		CPYFPN(&fe->fe_f2, &KLOG2);
470		/* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
471		d = fpu_add(fe);
472	}
473
474	return d;
475}
476
477struct fpn *
478fpu_log10(struct fpemu *fe)
479{
480	struct fpn *fp = &fe->fe_f2;
481	uint32_t fpsr;
482
483	fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
484
485	if (fp->fp_class >= FPC_NUM) {
486		if (fp->fp_sign) {	/* negative number or Inf */
487			fp = fpu_newnan(fe);
488			fpsr |= FPSR_OPERR;
489		} else if (fp->fp_class == FPC_NUM) {
490			/* the real work here */
491			fp = __fpu_logn(fe);
492			if (fp != &fe->fe_f1)
493				CPYFPN(&fe->fe_f1, fp);
494			(void)fpu_const(&fe->fe_f2, FPU_CONST_LN_10);
495			fp = fpu_div(fe);
496		} /* else if fp == +Inf, return +Inf */
497	} else if (fp->fp_class == FPC_ZERO) {
498		/* return -Inf */
499		fp->fp_class = FPC_INF;
500		fp->fp_sign = 1;
501		fpsr |= FPSR_DZ;
502	} else if (fp->fp_class == FPC_SNAN) {
503		fpsr |= FPSR_SNAN;
504		fp = fpu_newnan(fe);
505	} else {
506		fp = fpu_newnan(fe);
507	}
508
509	fe->fe_fpsr = fpsr;
510
511	return fp;
512}
513
514struct fpn *
515fpu_log2(struct fpemu *fe)
516{
517	struct fpn *fp = &fe->fe_f2;
518	uint32_t fpsr;
519
520	fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
521
522	if (fp->fp_class >= FPC_NUM) {
523		if (fp->fp_sign) {	/* negative number or Inf */
524			fp = fpu_newnan(fe);
525			fpsr |= FPSR_OPERR;
526		} else if (fp->fp_class == FPC_NUM) {
527			/* the real work here */
528			if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 &&
529			    fp->fp_mant[2] == 0) {
530				/* fp == 2.0 ^ exp <--> log2(fp) == exp */
531				fpu_explode(fe, &fe->fe_f3, FTYPE_LNG,
532				    &fp->fp_exp);
533				fp = &fe->fe_f3;
534			} else {
535				fp = __fpu_logn(fe);
536				if (fp != &fe->fe_f1)
537					CPYFPN(&fe->fe_f1, fp);
538				(void)fpu_const(&fe->fe_f2, FPU_CONST_LN_2);
539				fp = fpu_div(fe);
540			}
541		} /* else if fp == +Inf, return +Inf */
542	} else if (fp->fp_class == FPC_ZERO) {
543		/* return -Inf */
544		fp->fp_class = FPC_INF;
545		fp->fp_sign = 1;
546		fpsr |= FPSR_DZ;
547	} else if (fp->fp_class == FPC_SNAN) {
548		fpsr |= FPSR_SNAN;
549		fp = fpu_newnan(fe);
550	} else {
551		fp = fpu_newnan(fe);
552	}
553
554	fe->fe_fpsr = fpsr;
555	return fp;
556}
557
558struct fpn *
559fpu_logn(struct fpemu *fe)
560{
561	struct fpn *fp = &fe->fe_f2;
562	uint32_t fpsr;
563
564	fpsr = fe->fe_fpsr & ~FPSR_EXCP;	/* clear all exceptions */
565
566	if (fp->fp_class >= FPC_NUM) {
567		if (fp->fp_sign) {	/* negative number or Inf */
568			fp = fpu_newnan(fe);
569			fpsr |= FPSR_OPERR;
570		} else if (fp->fp_class == FPC_NUM) {
571			/* the real work here */
572			fp = __fpu_logn(fe);
573		} /* else if fp == +Inf, return +Inf */
574	} else if (fp->fp_class == FPC_ZERO) {
575		/* return -Inf */
576		fp->fp_class = FPC_INF;
577		fp->fp_sign = 1;
578		fpsr |= FPSR_DZ;
579	} else if (fp->fp_class == FPC_SNAN) {
580		fpsr |= FPSR_SNAN;
581		fp = fpu_newnan(fe);
582	} else {
583		fp = fpu_newnan(fe);
584	}
585
586	fe->fe_fpsr = fpsr;
587
588	return fp;
589}
590
591struct fpn *
592fpu_lognp1(struct fpemu *fe)
593{
594	struct fpn *fp;
595
596	/* if src is +0/-0, return +0/-0 */
597	if (ISZERO(&fe->fe_f2))
598		return &fe->fe_f2;
599
600	/* build a 1.0 */
601	fp = fpu_const(&fe->fe_f1, FPU_CONST_1);
602	/* fp = 1.0 + f2 */
603	fp = fpu_add(fe);
604
605	/* copy the result to the src opr */
606	CPYFPN(&fe->fe_f2, fp);
607
608	return fpu_logn(fe);
609}
610