Annotation of sys/arch/m68k/fpe/fpu_log.c, Revision 1.1.1.1
1.1 nbrk 1: /* $OpenBSD: fpu_log.c,v 1.6 2006/06/11 20:43:28 miod Exp $ */
2: /* $NetBSD: fpu_log.c,v 1.8 2003/07/15 02:43:10 lukem Exp $ */
3:
4: /*
5: * Copyright (c) 1995 Ken Nakata
6: * All rights reserved.
7: *
8: * Redistribution and use in source and binary forms, with or without
9: * modification, are permitted provided that the following conditions
10: * are met:
11: * 1. Redistributions of source code must retain the above copyright
12: * notice, this list of conditions and the following disclaimer.
13: * 2. Redistributions in binary form must reproduce the above copyright
14: * notice, this list of conditions and the following disclaimer in the
15: * documentation and/or other materials provided with the distribution.
16: * 3. Neither the name of the author nor the names of its contributors
17: * may be used to endorse or promote products derived from this software
18: * without specific prior written permission.
19: *
20: * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
21: * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23: * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
24: * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25: * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26: * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27: * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28: * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29: * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30: * SUCH DAMAGE.
31: *
32: * @(#)fpu_log.c 10/8/95
33: */
34:
35: #include <sys/types.h>
36: #include <sys/systm.h>
37:
38: #include <m68k/fpe/fpu_emulate.h>
39:
40: static u_int logA6[] = { 0x3FC2499A, 0xB5E4040B };
41: static u_int logA5[] = { 0xBFC555B5, 0x848CB7DB };
42: static u_int logA4[] = { 0x3FC99999, 0x987D8730 };
43: static u_int logA3[] = { 0xBFCFFFFF, 0xFF6F7E97 };
44: static u_int logA2[] = { 0x3FD55555, 0x555555A4 };
45: static u_int logA1[] = { 0xBFE00000, 0x00000008 };
46:
47: static u_int logB5[] = { 0x3F175496, 0xADD7DAD6 };
48: static u_int logB4[] = { 0x3F3C71C2, 0xFE80C7E0 };
49: static u_int logB3[] = { 0x3F624924, 0x928BCCFF };
50: static u_int logB2[] = { 0x3F899999, 0x999995EC };
51: static u_int logB1[] = { 0x3FB55555, 0x55555555 };
52:
53: /* sfpn = shortened fp number; can represent only positive numbers */
54: static struct sfpn {
55: int sp_exp;
56: u_int sp_m0, sp_m1;
57: } logtbl[] = {
58: { 0x3FFE - 0x3fff, 0xFE03F80FU, 0xE03F80FEU },
59: { 0x3FF7 - 0x3fff, 0xFF015358U, 0x833C47E2U },
60: { 0x3FFE - 0x3fff, 0xFA232CF2U, 0x52138AC0U },
61: { 0x3FF9 - 0x3fff, 0xBDC8D83EU, 0xAD88D549U },
62: { 0x3FFE - 0x3fff, 0xF6603D98U, 0x0F6603DAU },
63: { 0x3FFA - 0x3fff, 0x9CF43DCFU, 0xF5EAFD48U },
64: { 0x3FFE - 0x3fff, 0xF2B9D648U, 0x0F2B9D65U },
65: { 0x3FFA - 0x3fff, 0xDA16EB88U, 0xCB8DF614U },
66: { 0x3FFE - 0x3fff, 0xEF2EB71FU, 0xC4345238U },
67: { 0x3FFB - 0x3fff, 0x8B29B775U, 0x1BD70743U },
68: { 0x3FFE - 0x3fff, 0xEBBDB2A5U, 0xC1619C8CU },
69: { 0x3FFB - 0x3fff, 0xA8D839F8U, 0x30C1FB49U },
70: { 0x3FFE - 0x3fff, 0xE865AC7BU, 0x7603A197U },
71: { 0x3FFB - 0x3fff, 0xC61A2EB1U, 0x8CD907ADU },
72: { 0x3FFE - 0x3fff, 0xE525982AU, 0xF70C880EU },
73: { 0x3FFB - 0x3fff, 0xE2F2A47AU, 0xDE3A18AFU },
74: { 0x3FFE - 0x3fff, 0xE1FC780EU, 0x1FC780E2U },
75: { 0x3FFB - 0x3fff, 0xFF64898EU, 0xDF55D551U },
76: { 0x3FFE - 0x3fff, 0xDEE95C4CU, 0xA037BA57U },
77: { 0x3FFC - 0x3fff, 0x8DB956A9U, 0x7B3D0148U },
78: { 0x3FFE - 0x3fff, 0xDBEB61EEU, 0xD19C5958U },
79: { 0x3FFC - 0x3fff, 0x9B8FE100U, 0xF47BA1DEU },
80: { 0x3FFE - 0x3fff, 0xD901B203U, 0x6406C80EU },
81: { 0x3FFC - 0x3fff, 0xA9372F1DU, 0x0DA1BD17U },
82: { 0x3FFE - 0x3fff, 0xD62B80D6U, 0x2B80D62CU },
83: { 0x3FFC - 0x3fff, 0xB6B07F38U, 0xCE90E46BU },
84: { 0x3FFE - 0x3fff, 0xD3680D36U, 0x80D3680DU },
85: { 0x3FFC - 0x3fff, 0xC3FD0329U, 0x06488481U },
86: { 0x3FFE - 0x3fff, 0xD0B69FCBU, 0xD2580D0BU },
87: { 0x3FFC - 0x3fff, 0xD11DE0FFU, 0x15AB18CAU },
88: { 0x3FFE - 0x3fff, 0xCE168A77U, 0x25080CE1U },
89: { 0x3FFC - 0x3fff, 0xDE1433A1U, 0x6C66B150U },
90: { 0x3FFE - 0x3fff, 0xCB8727C0U, 0x65C393E0U },
91: { 0x3FFC - 0x3fff, 0xEAE10B5AU, 0x7DDC8ADDU },
92: { 0x3FFE - 0x3fff, 0xC907DA4EU, 0x871146ADU },
93: { 0x3FFC - 0x3fff, 0xF7856E5EU, 0xE2C9B291U },
94: { 0x3FFE - 0x3fff, 0xC6980C69U, 0x80C6980CU },
95: { 0x3FFD - 0x3fff, 0x82012CA5U, 0xA68206D7U },
96: { 0x3FFE - 0x3fff, 0xC4372F85U, 0x5D824CA6U },
97: { 0x3FFD - 0x3fff, 0x882C5FCDU, 0x7256A8C5U },
98: { 0x3FFE - 0x3fff, 0xC1E4BBD5U, 0x95F6E947U },
99: { 0x3FFD - 0x3fff, 0x8E44C60BU, 0x4CCFD7DEU },
100: { 0x3FFE - 0x3fff, 0xBFA02FE8U, 0x0BFA02FFU },
101: { 0x3FFD - 0x3fff, 0x944AD09EU, 0xF4351AF6U },
102: { 0x3FFE - 0x3fff, 0xBD691047U, 0x07661AA3U },
103: { 0x3FFD - 0x3fff, 0x9A3EECD4U, 0xC3EAA6B2U },
104: { 0x3FFE - 0x3fff, 0xBB3EE721U, 0xA54D880CU },
105: { 0x3FFD - 0x3fff, 0xA0218434U, 0x353F1DE8U },
106: { 0x3FFE - 0x3fff, 0xB92143FAU, 0x36F5E02EU },
107: { 0x3FFD - 0x3fff, 0xA5F2FCABU, 0xBBC506DAU },
108: { 0x3FFE - 0x3fff, 0xB70FBB5AU, 0x19BE3659U },
109: { 0x3FFD - 0x3fff, 0xABB3B8BAU, 0x2AD362A5U },
110: { 0x3FFE - 0x3fff, 0xB509E68AU, 0x9B94821FU },
111: { 0x3FFD - 0x3fff, 0xB1641795U, 0xCE3CA97BU },
112: { 0x3FFE - 0x3fff, 0xB30F6352U, 0x8917C80BU },
113: { 0x3FFD - 0x3fff, 0xB7047551U, 0x5D0F1C61U },
114: { 0x3FFE - 0x3fff, 0xB11FD3B8U, 0x0B11FD3CU },
115: { 0x3FFD - 0x3fff, 0xBC952AFEU, 0xEA3D13E1U },
116: { 0x3FFE - 0x3fff, 0xAF3ADDC6U, 0x80AF3ADEU },
117: { 0x3FFD - 0x3fff, 0xC2168ED0U, 0xF458BA4AU },
118: { 0x3FFE - 0x3fff, 0xAD602B58U, 0x0AD602B6U },
119: { 0x3FFD - 0x3fff, 0xC788F439U, 0xB3163BF1U },
120: { 0x3FFE - 0x3fff, 0xAB8F69E2U, 0x8359CD11U },
121: { 0x3FFD - 0x3fff, 0xCCECAC08U, 0xBF04565DU },
122: { 0x3FFE - 0x3fff, 0xA9C84A47U, 0xA07F5638U },
123: { 0x3FFD - 0x3fff, 0xD2420487U, 0x2DD85160U },
124: { 0x3FFE - 0x3fff, 0xA80A80A8U, 0x0A80A80BU },
125: { 0x3FFD - 0x3fff, 0xD7894992U, 0x3BC3588AU },
126: { 0x3FFE - 0x3fff, 0xA655C439U, 0x2D7B73A8U },
127: { 0x3FFD - 0x3fff, 0xDCC2C4B4U, 0x9887DACCU },
128: { 0x3FFE - 0x3fff, 0xA4A9CF1DU, 0x96833751U },
129: { 0x3FFD - 0x3fff, 0xE1EEBD3EU, 0x6D6A6B9EU },
130: { 0x3FFE - 0x3fff, 0xA3065E3FU, 0xAE7CD0E0U },
131: { 0x3FFD - 0x3fff, 0xE70D785CU, 0x2F9F5BDCU },
132: { 0x3FFE - 0x3fff, 0xA16B312EU, 0xA8FC377DU },
133: { 0x3FFD - 0x3fff, 0xEC1F392CU, 0x5179F283U },
134: { 0x3FFE - 0x3fff, 0x9FD809FDU, 0x809FD80AU },
135: { 0x3FFD - 0x3fff, 0xF12440D3U, 0xE36130E6U },
136: { 0x3FFE - 0x3fff, 0x9E4CAD23U, 0xDD5F3A20U },
137: { 0x3FFD - 0x3fff, 0xF61CCE92U, 0x346600BBU },
138: { 0x3FFE - 0x3fff, 0x9CC8E160U, 0xC3FB19B9U },
139: { 0x3FFD - 0x3fff, 0xFB091FD3U, 0x8145630AU },
140: { 0x3FFE - 0x3fff, 0x9B4C6F9EU, 0xF03A3CAAU },
141: { 0x3FFD - 0x3fff, 0xFFE97042U, 0xBFA4C2ADU },
142: { 0x3FFE - 0x3fff, 0x99D722DAU, 0xBDE58F06U },
143: { 0x3FFE - 0x3fff, 0x825EFCEDU, 0x49369330U },
144: { 0x3FFE - 0x3fff, 0x9868C809U, 0x868C8098U },
145: { 0x3FFE - 0x3fff, 0x84C37A7AU, 0xB9A905C9U },
146: { 0x3FFE - 0x3fff, 0x97012E02U, 0x5C04B809U },
147: { 0x3FFE - 0x3fff, 0x87224C2EU, 0x8E645FB7U },
148: { 0x3FFE - 0x3fff, 0x95A02568U, 0x095A0257U },
149: { 0x3FFE - 0x3fff, 0x897B8CACU, 0x9F7DE298U },
150: { 0x3FFE - 0x3fff, 0x94458094U, 0x45809446U },
151: { 0x3FFE - 0x3fff, 0x8BCF55DEU, 0xC4CD05FEU },
152: { 0x3FFE - 0x3fff, 0x92F11384U, 0x0497889CU },
153: { 0x3FFE - 0x3fff, 0x8E1DC0FBU, 0x89E125E5U },
154: { 0x3FFE - 0x3fff, 0x91A2B3C4U, 0xD5E6F809U },
155: { 0x3FFE - 0x3fff, 0x9066E68CU, 0x955B6C9BU },
156: { 0x3FFE - 0x3fff, 0x905A3863U, 0x3E06C43BU },
157: { 0x3FFE - 0x3fff, 0x92AADE74U, 0xC7BE59E0U },
158: { 0x3FFE - 0x3fff, 0x8F1779D9U, 0xFDC3A219U },
159: { 0x3FFE - 0x3fff, 0x94E9BFF6U, 0x15845643U },
160: { 0x3FFE - 0x3fff, 0x8DDA5202U, 0x37694809U },
161: { 0x3FFE - 0x3fff, 0x9723A1B7U, 0x20134203U },
162: { 0x3FFE - 0x3fff, 0x8CA29C04U, 0x6514E023U },
163: { 0x3FFE - 0x3fff, 0x995899C8U, 0x90EB8990U },
164: { 0x3FFE - 0x3fff, 0x8B70344AU, 0x139BC75AU },
165: { 0x3FFE - 0x3fff, 0x9B88BDAAU, 0x3A3DAE2FU },
166: { 0x3FFE - 0x3fff, 0x8A42F870U, 0x5669DB46U },
167: { 0x3FFE - 0x3fff, 0x9DB4224FU, 0xFFE1157CU },
168: { 0x3FFE - 0x3fff, 0x891AC73AU, 0xE9819B50U },
169: { 0x3FFE - 0x3fff, 0x9FDADC26U, 0x8B7A12DAU },
170: { 0x3FFE - 0x3fff, 0x87F78087U, 0xF78087F8U },
171: { 0x3FFE - 0x3fff, 0xA1FCFF17U, 0xCE733BD4U },
172: { 0x3FFE - 0x3fff, 0x86D90544U, 0x7A34ACC6U },
173: { 0x3FFE - 0x3fff, 0xA41A9E8FU, 0x5446FB9FU },
174: { 0x3FFE - 0x3fff, 0x85BF3761U, 0x2CEE3C9BU },
175: { 0x3FFE - 0x3fff, 0xA633CD7EU, 0x6771CD8BU },
176: { 0x3FFE - 0x3fff, 0x84A9F9C8U, 0x084A9F9DU },
177: { 0x3FFE - 0x3fff, 0xA8489E60U, 0x0B435A5EU },
178: { 0x3FFE - 0x3fff, 0x83993052U, 0x3FBE3368U },
179: { 0x3FFE - 0x3fff, 0xAA59233CU, 0xCCA4BD49U },
180: { 0x3FFE - 0x3fff, 0x828CBFBEU, 0xB9A020A3U },
181: { 0x3FFE - 0x3fff, 0xAC656DAEU, 0x6BCC4985U },
182: { 0x3FFE - 0x3fff, 0x81848DA8U, 0xFAF0D277U },
183: { 0x3FFE - 0x3fff, 0xAE6D8EE3U, 0x60BB2468U },
184: { 0x3FFE - 0x3fff, 0x80808080U, 0x80808081U },
185: { 0x3FFE - 0x3fff, 0xB07197A2U, 0x3C46C654U },
186: };
187:
188: struct fpn *__fpu_logn(struct fpemu *fe);
189:
190: /*
191: * natural log - algorithm taken from Motorola FPSP,
192: * except this doesn't bother to check for invalid input.
193: */
194: struct fpn *
195: __fpu_logn(fe)
196: struct fpemu *fe;
197: {
198: static struct fpn X, F, U, V, W, KLOG2;
199: struct fpn *d;
200: int i, k;
201:
202: CPYFPN(&X, &fe->fe_f2);
203:
204: /* see if |X-1| < 1/16 approx. */
205: if ((-1 == X.fp_exp && (0xf07d0000U >> (31 - FP_LG)) <= X.fp_mant[0]) ||
206: (0 == X.fp_exp && X.fp_mant[0] <= (0x88410000U >> (31 - FP_LG)))) {
207: /* log near 1 */
208: #if FPE_DEBUG
209: printf("__fpu_logn: log near 1\n");
210: #endif
211:
212: fpu_const(&fe->fe_f1, 0x32);
213: /* X+1 */
214: d = fpu_add(fe);
215: CPYFPN(&V, d);
216:
217: CPYFPN(&fe->fe_f1, &X);
218: fpu_const(&fe->fe_f2, 0x32); /* 1.0 */
219: fe->fe_f2.fp_sign = 1; /* -1.0 */
220: /* X-1 */
221: d = fpu_add(fe);
222: CPYFPN(&fe->fe_f1, d);
223: /* 2(X-1) */
224: fe->fe_f1.fp_exp++; /* *= 2 */
225: CPYFPN(&fe->fe_f2, &V);
226: /* U=2(X-1)/(X+1) */
227: d = fpu_div(fe);
228: CPYFPN(&U, d);
229: CPYFPN(&fe->fe_f1, d);
230: CPYFPN(&fe->fe_f2, d);
231: /* V=U*U */
232: d = fpu_mul(fe);
233: CPYFPN(&V, d);
234: CPYFPN(&fe->fe_f1, d);
235: CPYFPN(&fe->fe_f2, d);
236: /* W=V*V */
237: d = fpu_mul(fe);
238: CPYFPN(&W, d);
239:
240: /* calculate U+U*V*([B1+W*(B3+W*B5)]+[V*(B2+W*B4)]) */
241:
242: /* B1+W*(B3+W*B5) part */
243: CPYFPN(&fe->fe_f1, d);
244: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB5);
245: /* W*B5 */
246: d = fpu_mul(fe);
247: CPYFPN(&fe->fe_f1, d);
248: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB3);
249: /* B3+W*B5 */
250: d = fpu_add(fe);
251: CPYFPN(&fe->fe_f1, d);
252: CPYFPN(&fe->fe_f2, &W);
253: /* W*(B3+W*B5) */
254: d = fpu_mul(fe);
255: CPYFPN(&fe->fe_f1, d);
256: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB1);
257: /* B1+W*(B3+W*B5) */
258: d = fpu_add(fe);
259: CPYFPN(&X, d);
260:
261: /* [V*(B2+W*B4)] part */
262: CPYFPN(&fe->fe_f1, &W);
263: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB4);
264: /* W*B4 */
265: d = fpu_mul(fe);
266: CPYFPN(&fe->fe_f1, d);
267: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logB2);
268: /* B2+W*B4 */
269: d = fpu_add(fe);
270: CPYFPN(&fe->fe_f1, d);
271: CPYFPN(&fe->fe_f2, &V);
272: /* V*(B2+W*B4) */
273: d = fpu_mul(fe);
274: CPYFPN(&fe->fe_f1, d);
275: CPYFPN(&fe->fe_f2, &X);
276: /* B1+W*(B3+W*B5)+V*(B2+W*B4) */
277: d = fpu_add(fe);
278: CPYFPN(&fe->fe_f1, d);
279: CPYFPN(&fe->fe_f2, &V);
280: /* V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
281: d = fpu_mul(fe);
282: CPYFPN(&fe->fe_f1, d);
283: CPYFPN(&fe->fe_f2, &U);
284: /* U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
285: d = fpu_mul(fe);
286: CPYFPN(&fe->fe_f1, d);
287: CPYFPN(&fe->fe_f2, &U);
288: /* U+U*V*(B1+W*(B3+W*B5)+V*(B2+W*B4)) */
289: d = fpu_add(fe);
290: } else /* the usual case */ {
291: #if FPE_DEBUG
292: printf("__fpu_logn: the usual case. X=(%d,%08x,%08x...)\n",
293: X.fp_exp, X.fp_mant[0], X.fp_mant[1]);
294: #endif
295:
296: k = X.fp_exp;
297: /* X <- Y */
298: X.fp_exp = fe->fe_f2.fp_exp = 0;
299:
300: /* get the most significant 7 bits of X */
301: F.fp_class = FPC_NUM;
302: F.fp_sign = 0;
303: F.fp_exp = X.fp_exp;
304: F.fp_mant[0] = X.fp_mant[0] & (0xfe000000U >> (31 - FP_LG));
305: F.fp_mant[0] |= (0x01000000U >> (31 - FP_LG));
306: F.fp_mant[1] = F.fp_mant[2] = 0;
307: F.fp_sticky = 0;
308:
309: #if FPE_DEBUG
310: printf("__fpu_logn: X=Y*2^k=(%d,%08x,%08x...)*2^%d\n",
311: fe->fe_f2.fp_exp, fe->fe_f2.fp_mant[0],
312: fe->fe_f2.fp_mant[1], k);
313: printf("__fpu_logn: F=(%d,%08x,%08x...)\n",
314: F.fp_exp, F.fp_mant[0], F.fp_mant[1]);
315: #endif
316:
317: /* index to the table */
318: i = (F.fp_mant[0] >> (FP_LG - 7)) & 0x7e;
319:
320: #if FPE_DEBUG
321: printf("__fpu_logn: index to logtbl i=%d(%x)\n", i, i);
322: #endif
323:
324: CPYFPN(&fe->fe_f1, &F);
325: /* -F */
326: fe->fe_f1.fp_sign = 1;
327: /* Y-F */
328: d = fpu_add(fe);
329: CPYFPN(&fe->fe_f1, d);
330:
331: /* fe_f2 = 1/F */
332: fe->fe_f2.fp_class = FPC_NUM;
333: fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
334: fe->fe_f2.fp_exp = logtbl[i].sp_exp;
335: fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
336: fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
337: (logtbl[i].sp_m1 >> (31 - FP_LG));
338: fe->fe_f2.fp_mant[2] = (u_int)(logtbl[i].sp_m1 << (FP_LG + 1));
339:
340: #if FPE_DEBUG
341: printf("__fpu_logn: 1/F=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
342: fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
343: #endif
344:
345: /* U = (Y-F) * (1/F) */
346: d = fpu_mul(fe);
347: CPYFPN(&U, d);
348:
349: /* KLOG2 = K * ln(2) */
350: /* fe_f1 == (fpn)k */
351: fpu_explode(fe, &fe->fe_f1, FTYPE_LNG, &k);
352: (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
353: #if FPE_DEBUG
354: printf("__fpu_logn: fp(k)=(%d,%08x,%08x...)\n", fe->fe_f1.fp_exp,
355: fe->fe_f1.fp_mant[0], fe->fe_f1.fp_mant[1]);
356: printf("__fpu_logn: ln(2)=(%d,%08x,%08x...)\n", fe->fe_f2.fp_exp,
357: fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
358: #endif
359: /* K * LOGOF2 */
360: d = fpu_mul(fe);
361: CPYFPN(&KLOG2, d);
362:
363: /* V=U*U */
364: CPYFPN(&fe->fe_f1, &U);
365: CPYFPN(&fe->fe_f2, &U);
366: d = fpu_mul(fe);
367: CPYFPN(&V, d);
368:
369: /*
370: * approximation of LOG(1+U) by
371: * (U+V*(A1+V*(A3+V*A5)))+(U*V*(A2+V*(A4+V*A6)))
372: */
373:
374: /* (U+V*(A1+V*(A3+V*A5))) part */
375: CPYFPN(&fe->fe_f1, d);
376: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA5);
377: /* V*A5 */
378: d = fpu_mul(fe);
379:
380: CPYFPN(&fe->fe_f1, d);
381: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA3);
382: /* A3+V*A5 */
383: d = fpu_add(fe);
384:
385: CPYFPN(&fe->fe_f1, d);
386: CPYFPN(&fe->fe_f2, &V);
387: /* V*(A3+V*A5) */
388: d = fpu_mul(fe);
389:
390: CPYFPN(&fe->fe_f1, d);
391: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA1);
392: /* A1+V*(A3+V*A5) */
393: d = fpu_add(fe);
394:
395: CPYFPN(&fe->fe_f1, d);
396: CPYFPN(&fe->fe_f2, &V);
397: /* V*(A1+V*(A3+V*A5)) */
398: d = fpu_mul(fe);
399:
400: CPYFPN(&fe->fe_f1, d);
401: CPYFPN(&fe->fe_f2, &U);
402: /* U+V*(A1+V*(A3+V*A5)) */
403: d = fpu_add(fe);
404:
405: CPYFPN(&X, d);
406:
407: /* (U*V*(A2+V*(A4+V*A6))) part */
408: CPYFPN(&fe->fe_f1, &V);
409: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA6);
410: /* V*A6 */
411: d = fpu_mul(fe);
412: CPYFPN(&fe->fe_f1, d);
413: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA4);
414: /* A4+V*A6 */
415: d = fpu_add(fe);
416: CPYFPN(&fe->fe_f1, d);
417: CPYFPN(&fe->fe_f2, &V);
418: /* V*(A4+V*A6) */
419: d = fpu_mul(fe);
420: CPYFPN(&fe->fe_f1, d);
421: fpu_explode(fe, &fe->fe_f2, FTYPE_DBL, logA2);
422: /* A2+V*(A4+V*A6) */
423: d = fpu_add(fe);
424: CPYFPN(&fe->fe_f1, d);
425: CPYFPN(&fe->fe_f2, &V);
426: /* V*(A2+V*(A4+V*A6)) */
427: d = fpu_mul(fe);
428: CPYFPN(&fe->fe_f1, d);
429: CPYFPN(&fe->fe_f2, &U);
430: /* U*V*(A2+V*(A4+V*A6)) */
431: d = fpu_mul(fe);
432: CPYFPN(&fe->fe_f1, d);
433: i++;
434: /* fe_f2 = logtbl[i+1] (== LOG(F)) */
435: fe->fe_f2.fp_class = FPC_NUM;
436: fe->fe_f2.fp_sign = fe->fe_f2.fp_sticky = fe->fe_f2.fp_mant[2] = 0;
437: fe->fe_f2.fp_exp = logtbl[i].sp_exp;
438: fe->fe_f2.fp_mant[0] = (logtbl[i].sp_m0 >> (31 - FP_LG));
439: fe->fe_f2.fp_mant[1] = (logtbl[i].sp_m0 << (FP_LG + 1)) |
440: (logtbl[i].sp_m1 >> (31 - FP_LG));
441: fe->fe_f2.fp_mant[2] = (logtbl[i].sp_m1 << (FP_LG + 1));
442:
443: #if FPE_DEBUG
444: printf("__fpu_logn: ln(F)=(%d,%08x,%08x,...)\n", fe->fe_f2.fp_exp,
445: fe->fe_f2.fp_mant[0], fe->fe_f2.fp_mant[1]);
446: #endif
447:
448: /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */
449: d = fpu_add(fe);
450: CPYFPN(&fe->fe_f1, d);
451: CPYFPN(&fe->fe_f2, &X);
452: /* LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
453: d = fpu_add(fe);
454:
455: #if FPE_DEBUG
456: printf("__fpu_logn: ln(Y)=(%c,%d,%08x,%08x,%08x)\n",
457: d->fp_sign ? '-' : '+', d->fp_exp,
458: d->fp_mant[0], d->fp_mant[1], d->fp_mant[2]);
459: #endif
460:
461: CPYFPN(&fe->fe_f1, d);
462: CPYFPN(&fe->fe_f2, &KLOG2);
463: /* K*LOGOF2+LOG(F)+U+V*(A1+V*(A3+V*A5))+U*V*(A2+V*(A4+V*A6)) */
464: d = fpu_add(fe);
465: }
466:
467: return d;
468: }
469:
470: struct fpn *
471: fpu_log10(fe)
472: struct fpemu *fe;
473: {
474: struct fpn *fp = &fe->fe_f2;
475: u_int fpsr;
476:
477: fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */
478:
479: if (fp->fp_class >= FPC_NUM) {
480: if (fp->fp_sign) { /* negative number or Inf */
481: fp = fpu_newnan(fe);
482: fpsr |= FPSR_OPERR;
483: } else if (fp->fp_class == FPC_NUM) {
484: /* the real work here */
485: fp = __fpu_logn(fe);
486: if (fp != &fe->fe_f1)
487: CPYFPN(&fe->fe_f1, fp);
488: (void)fpu_const(&fe->fe_f2, 0x31 /* ln(10) */);
489: fp = fpu_div(fe);
490: } /* else if fp == +Inf, return +Inf */
491: } else if (fp->fp_class == FPC_ZERO) {
492: /* return -Inf */
493: fp->fp_class = FPC_INF;
494: fp->fp_sign = 1;
495: fpsr |= FPSR_DZ;
496: } else if (fp->fp_class == FPC_SNAN) {
497: fpsr |= FPSR_SNAN;
498: fp = fpu_newnan(fe);
499: } else {
500: fp = fpu_newnan(fe);
501: }
502:
503: fe->fe_fpsr = fpsr;
504:
505: return fp;
506: }
507:
508: struct fpn *
509: fpu_log2(fe)
510: struct fpemu *fe;
511: {
512: struct fpn *fp = &fe->fe_f2;
513: u_int fpsr;
514:
515: fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */
516:
517: if (fp->fp_class >= FPC_NUM) {
518: if (fp->fp_sign) { /* negative number or Inf */
519: fp = fpu_newnan(fe);
520: fpsr |= FPSR_OPERR;
521: } else if (fp->fp_class == FPC_NUM) {
522: /* the real work here */
523: if (fp->fp_mant[0] == FP_1 && fp->fp_mant[1] == 0 &&
524: fp->fp_mant[2] == 0) {
525: /* fp == 2.0 ^ exp <--> log2(fp) == exp */
526: fpu_explode(fe, &fe->fe_f3, FTYPE_LNG, &fp->fp_exp);
527: fp = &fe->fe_f3;
528: } else {
529: fp = __fpu_logn(fe);
530: if (fp != &fe->fe_f1)
531: CPYFPN(&fe->fe_f1, fp);
532: (void)fpu_const(&fe->fe_f2, 0x30 /* ln(2) */);
533: fp = fpu_div(fe);
534: }
535: } /* else if fp == +Inf, return +Inf */
536: } else if (fp->fp_class == FPC_ZERO) {
537: /* return -Inf */
538: fp->fp_class = FPC_INF;
539: fp->fp_sign = 1;
540: fpsr |= FPSR_DZ;
541: } else if (fp->fp_class == FPC_SNAN) {
542: fpsr |= FPSR_SNAN;
543: fp = fpu_newnan(fe);
544: } else {
545: fp = fpu_newnan(fe);
546: }
547:
548: fe->fe_fpsr = fpsr;
549: return fp;
550: }
551:
552: struct fpn *
553: fpu_logn(fe)
554: struct fpemu *fe;
555: {
556: struct fpn *fp = &fe->fe_f2;
557: u_int fpsr;
558:
559: fpsr = fe->fe_fpsr & ~FPSR_EXCP; /* clear all exceptions */
560:
561: if (fp->fp_class >= FPC_NUM) {
562: if (fp->fp_sign) { /* negative number or Inf */
563: fp = fpu_newnan(fe);
564: fpsr |= FPSR_OPERR;
565: } else if (fp->fp_class == FPC_NUM) {
566: /* the real work here */
567: fp = __fpu_logn(fe);
568: } /* else if fp == +Inf, return +Inf */
569: } else if (fp->fp_class == FPC_ZERO) {
570: /* return -Inf */
571: fp->fp_class = FPC_INF;
572: fp->fp_sign = 1;
573: fpsr |= FPSR_DZ;
574: } else if (fp->fp_class == FPC_SNAN) {
575: fpsr |= FPSR_SNAN;
576: fp = fpu_newnan(fe);
577: } else {
578: fp = fpu_newnan(fe);
579: }
580:
581: fe->fe_fpsr = fpsr;
582:
583: return fp;
584: }
585:
586: struct fpn *
587: fpu_lognp1(fe)
588: struct fpemu *fe;
589: {
590: struct fpn *fp;
591:
592: /* build a 1.0 */
593: fp = fpu_const(&fe->fe_f1, 0x32); /* get 1.0 */
594: /* fp = 1.0 + f2 */
595: fp = fpu_add(fe);
596:
597: /* copy the result to the src opr */
598: if (&fe->fe_f2 != fp)
599: CPYFPN(&fe->fe_f2, fp);
600:
601: return fpu_logn(fe);
602: }
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